Plot armour

I am talking from experience with computer games rather than with D&D, but the general idea of being somewhere out of your depth and only ever 1 decision from death is the same. The premise of this is that you want your players to get attached to their characters rather than the plot.

So you create something that means death is not permanent, so they can always recover.

Examples:

They are already dead, and just souls trapped in the hells. Maybe they are owned by one devil already and as well as trying to navigate the politics they are trying to find a way back to the material plane and free their souls from whatever contract gives that devil ownership. Death therefore is just part of the eternal torment of the hells, and they reform wherever they are tethered.

Mysterious gem of saving them in the nick of time! I can't remember which game I stole this from, but they are teleported to a demiplane watched over by a mysterious creature who sends them back where they were after a rest.

Slight lore change. Devils can't permanently die when not on their home plane, in your world this applies in reverse to any creature not native to the hells, they simply re-appear somewhere when they die.

You can't have it all.

If the continuous player experience is important, then it needs to be easier to avoid the "wrong" choices, non-death consequences need to be prevalent, or death needs to become a lot less of an obstacle.

There are a variety of ways to accomplish any of those, but the core of the issue is that you can't have characters balanced on the knife's edge of mortal danger all the time without the very real risks of said mortal danger. But this is a game, and so it's expected that the balance will be generally tipped in the players' favor.

Avoiding the wrong choices

My number one suggestion is to provide lots of information to the players on what's going on and what the likely consequences of actions are. If there's a wrong side to align themselves with, and doing so will almost certainly lead to a TPK, then your players need to have enough information to identify that that side is the wrong one before they choose.

This may be difficult in a political intrigue-focused game, but you can find ways to convey relevant information incidentally. If players are being courted by the Order of Plot Cannon Fodder, perhaps you pepper the game with information about how that group's military forces are inferior to others', they have no good political leverage to use, they are seriously mistaken in some of their assumptions, and they don't actually have a plan that leads to success (i.e., phase 1: steal underpants; phase 2: …; phase 3: profits!). This works best if the game is strongly plotted, and factions are pre-destined to succeed or fail at specific times in specific ways.

If the setting is less rigid and you want player agency to matter more, then it should be less pre-defined for certain factions to be the wrong choices. It may be the case that either group A or group B will fall during the first chapter, but the players' involvement with one or the other will be decisive in which group it is that collapses. The one they choose is fundamentally right, because the next missions will be to damage the other group and lead to its downfall.

But if choosing the wrong option between A and B results in death (and the end of the story/experience you want to convey), then you aren't really presenting a choice. If there's no meaningful choice to be had, then don't pretend that there is just so that the players can effectively end the story early through arbitrary failure.

Intermediate consequences

This is the one I've used most in my politically-focused games. It's possible to soften the consequences of a wrong choice in many circumstances. In the heat of battle, bad decisions may well lead to PC death. But outside of that a pack of scheming, unscrupulous individuals might try to find other options. A party that makes a bad choice, angering the leader of group A, might lead to that leader killing them through means the party cannot resist. Or that leader might leverage the party's mistake as blackmail material, or a source of misinformation to foster, or imprison them for later use, or PCs are tortured in ways that have mechanical consequences (maybe a persistent stat penalty, disadvantage against certain creatures or groups, or something), or any number of other elements.

The point here being that while death may be a plausible, thematically appropriate outcome to mistakes you don't have to use it. PC death can still be an ever-present danger without being the sole danger the PCs face. I would imagine that in the Nine Hells there are many fates worse than death but which a PC might escape or be rescued from in some way.

Death is really just an inconvenience

This is my least favorite of the three options because I think it's hard to pull off well, but it definitely is an option. Many of the other answers have suggested approaches to this, so I won't rehash them here, but this is the ultimate backstop. If a TPK doesn't end the story or break character continuity, then the risk evaporates.

The major reason I don't like this option is that it imposes significant worldbuilding issues (as other answers also point out). An antagonist is unlikely to consider a TPK a good way to deal with the PCs after a wrong choice because that won't really hinder the PCs. As a result, NPCs assigning missions will probably not consider mortal risk to be at all important, and it would not be plausible for NPC antagonists to prefer killing to other alternatives (like permanent maiming and imprisonment).

The main point being that permanently stopping the PCs is almost certainly going to be the antagonists' goal. Normally a TPK will accomplish that, which is why antagonists try to kill PCs. If a TPK won't cut it, then antagonists won't put much effort into that approach and would instead focus on some alternative that will accomplish the same mechanical goal.

The other reason I don't like it is that it drains most of the tension from scenarios that D&D provides. Death is a serious, though not insurmountable, consequence and so players try to avoid it. The risk creates excitement and makes player choices meaningful. If the consequences of death are basically nothing at all, then that excitement is gone. It can be replaced with other sources of excitement, but that can be difficult to do. What would the PCs by trying to avoid if death is irrelevant?

Not everyone will die in a Party Kill, possibly.

Depending on how you approach your players, and by making it very clear to them, you can encourage a behavior of 'flee the minute someone gets decapitated'. This may encourage a sort of cowardness if people run from every fight, but if someone flees and they live to tell the tale they could simply revive their fallen allies or meet up with newer allies (Newer PC's) and more or less keep the story going as it had been, as long as the other players are not upset.

Just because everyone dies doesn't mean they won't be revived or used.

Are they fighting for or against Archdevils, either way...their deaths could lead to them being revived with a new issue: They now owe their souls or new lives to the devil in question.

Even stranger, perhaps they die and....not all that much happens. Their soul passes...straight to the Nine Hells, and they continue the adventure as a weird devil with all of their old memories and personality, but perhaps weaker and with odd obligations.

So to answer the question in specifics:
The way of having a continuous experience is by realizing that death, at these levels, is not the final stop for heroes and villains in most worlds.

This could be completely useless though if you dislike or don't use much resurrection magic.

The same way Game of Thrones does

By having a continuous plot line irrespective of the entry and exit of various characters.

This can be “You are no this guy, this is how the events to date have shaped your backstory but apart from that you have no agenda” or “You are now the son, daughter, wife, gynecologist of this dead guy and start with pretty much the same agenda.” Hopefully the dead characters have left some achievements to build on - Ned’s failure led to Rob’s failure led to Bran and Sanaa’s success.

Look, if you want realpolitik in your game you have to play it the way Cersi said - “If you play the game of thrones and lose, you die.” Big rewards, big stakes, big risks.

Tell the story in episodes with different protagonists

First a disclaimer, I have no idea about the Nine Hells, but I believe the question can be answered independently of the setting.

One option to present a world were instant death is always a possibility is to plan the story independent but related episodes that are telling a different part of the story.
Each episode features its own story arc and can be won or lost by the players.
Either way the story resets with a new set of characters of a different faction/background to tell a different aspect of the story.

The result of previous episodes influence some of the details of the following episodes, but because they are not a direct continuation it will work either way.

This way, you can even have the players play for opposing sides in the story, or encounter their previous characters (in case they survived) as NPCs or foes.

One example that comes to mind is the We Be Goblins Pathfinder module, which is a prequel to another campaign, in which the players play goblins in an one-shot adventure, which sets into movement the actual campaign.

https://paizo.com/products/btpy8j5w?Pathfinder-Module-We-Be-Goblins

Design a useful cosmology

So, what happens when you die? If it's just, like, oblivion or something that's 1) not very RAW compatible since you can be questioned and make decisions and raised from the dead and stuff and 2) a really easy way out of Hell for most of the souls trapped there. So the character just ending when you die is kind of a bad idea as a setting detail for this campaign.

On the other hand, characters generally are played like they don't want to die, even in Hell, so if we want to keep that we need a reason that dying is bad. Here is what I do for political games set in the afterlife in 3.5, I think it works just as well in 5e but I haven't run a political game set in the afterlife in 5e yet:

1) When creatures die, they go to their afterlife. Depending on the setting for any particular game the rules for how that's determined are different but in each case I have it be a process that takes the character's next turn and deposits their soul (which has the same stats as their normal form) on said plane in a location determined by rules particular to the campaign in question. For the purposes of your game, your players' afterlife is clearly the Nine Hells, so if they die they should respawn there, somewhere.

2) Death restores all hp and cures all afflictions. All ongoing spells etc end immediately. Death breaks concentration, though in some 5e games I let casters avoid that with a DC 25 concentration check.

3) Powerful creatures with a big stake in something may not back down just because you killed them. Normally in 3.5 games I run, for example, dragons will Plane Shift/Greater Teleport back into a fight a couple rounds after they are killed if they think they can win without dying a second time. In 5e games, this has been much less common because far fewer opponents have access to sufficently powerful magic, but I have used the Draconic Spellcasting variant with Plane Shift to discourage players from killing rather than incapacitating an Ancient Red Dragon. In a game about the politics of characters beyond the reach of a 15th level party set in the Nine Hells I would expect teleporting back into combat after being killed to be a lot more common, though, since all that would be needed is sufficient access to teleportation magic, which is a much lower level than Plane Shift.

4) So, in general, I houserule level-loss (and Con loss if 1st level) on all resurrection effects that aren't the 9th level spell True Resurrection instead of the new 5e penalties in pretty much all of my 5e games, because I think it's important that characters have some concern about death until the highest echelons of power. In the case of a game like this where you are playing in the afterlife, I find it important to rule that level loss occurs at death, not at resurrection, and that True Resurrection essentially lets a character gain a level back rather than preventing its loss in the first place. Monsters and other non-classed creatures lose HD instead of levels, and anything that, depending on who I'm playing with, hits either Con 0 or a negative Constitution score of sufficient magnitude to render its maximum hp 0 cannot be raised. This makes it possible to perma-kill characters by teleporting to wherever they respawn each time they do and then killing them again until eventually they stop coming back, but that's a lot of work and usually killing someone normally is enough to get them out of your way. It also prevents suicide-as-fast-travel, at least most of the time.

With these rules TPKs aren't usually too much of a problem for me, because the party can just regroup and put up with having failed a mission and lost a level rather than having to start a new campaign. There is still a risk of an actual TPK where the party doesn't merely die but actually screws themselves over so bad that they either don't die and are trapped in some endless living hell from which they can't escape or get somebody sufficiently powerful sent to track the party down and repeatedly kill them until they stay dead. In the former case I usually take some time and figure out some way to hand-wave an escape, but the latter can be hard to deal with. In any case, run of the mill 'a fight was too hard and now you're dead' TPKs aren't a problem with these rules implemented.

Provide players with something other than individual characters to invest in

When I GM, I prefer to do it in a very gloves-off fashion. The world is deadly and if the dice (or the inevitable consequences of an action) say you die, you die. So I regularly deal with the question of how to keep players invested in the game after the deaths of their characters.

My primary way of doing this is by giving them something larger than their characters to control and develop, as a higher-order focus of investment. In one campaign, the PCs were colonists, settling a new town on a just-discovered island. In another, they were cyberpunk runners who managed a small drone manufacturing company, seeking out new tech to improve their products or taking advantage of opportunities to sabotage their competitors. In either case, even if some or all of the PCs were to die, the town or the drone company survived, all of the previous characters' work to develop it remained, and new PCs could come in to continue that work.

Ars Magica is designed very much along these lines, with the PCs being members of a "Covenant" which is built up over decades of in-game time, while individual characters live, age, die (of old age if not by violence) or retire, and are replaced (sometimes even by their own children, given the long time scale of a campaign). Some materials even go so far as to suggest that, in an Ars Magica campaign, the Covenant is the real main character, shared by all the players.

In your specific Hellish case, the most obvious way to implement this would be for the PCs to be members of some sort of faction dedicated to bringing one or more arch-devils down, or perhaps with some other goal that requires a presence in the Nine Hells, which could be based in Hell itself (if you want them to be native) or on another plane with the means to send people to Hell and retrieve them after missions (if you want them to be "intruders"). The important thing is for the players to be in control of the organization that the PCs belong to, so that they'll be invested in the organization, its goals, its plans, and its ongoing development.

The Stars Without Number supplements Darkness Visible (espionage) and Starvation Cheap (military) are good examples of this approach, with each player having a "staff" character who is roleplayed between adventures, guiding the players' spy agency or military unit, and a "field operative" character who actually goes out on missions and plays in adventures.

Aside from player investment, you also raised the issue of character knowledge carrying on after a potential TPK. Cyberpunk- and transhuman-genre games generally deal with this by having some sort of memory-recorder implant which can be used to download the dead character's knowledge after their demise. A magical memory crystal could serve this purpose in a fantasy game, although it obviously lends a flavor which may be unwanted.

An alternate approach which is less likely to give a "magical cyberpunk" feel to the game would be to provide a means for the PCs to be in constant, or at least frequent, communication with their home base - a Stone of Far Speech, Sending spells, clandestine meetings with NPC messenger agents, dead drops of written reports, etc. - which would then allow replacement characters to be briefed on the information gathered by the previous PCs.

They could have access to the Clone spell, and have your permission, as DM, to abuse it. They could all die in a TPK, and whoever had a clone prepared in advance survives.

This wouldn't prevent PC's from ever dying, because an enemy might seek out their clones and destroy them before killing the PC, but it means they won't be accidentally killed by random enemies.

Clone is only available to wizards 15th level or higher, but that fits with your current campaign setting. If none of the PC's are a wizard, they can seek out an NPC wizard capable of casting clone.