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This question reminded me of a very vaguely recalled short story, most likely from the early '00s or '90s (and probably in a magazine like F&SF, Asimov's or Analog), of a space ship that can easily travel incredibly far, galaxies clusters away, in some far future when humans commonly can and do pilot craft that travel above c somehow (I don't recall if this involved some sort of hyperspace or what), colonizing the universe with abandon.

Somehow (obviously this seems incredibly improbable, but I don't recall how this was explained -- perhaps ships had some light-speed-breaking way of detecting other ships?) the handful (2? 3?) people in a first ship randomly encounter in mid-intergalactic-space another human traveler traveling alone in his own ship, and they dock the two ships together. I think they have dinner together in honor of the meeting, but something is off about their new acquaintance (some wort of craziness that slowly reveals itself?), and some sort of conflict occurs.

I think someone on the first ship was working on something like simulating a miniature universe in a computer.

The story got... weird, somehow... toward the end. I think just one character somehow got locked into one of the ships with the controls jammed into taking him far beyond the furthest explored reaches of the universe, and he was just left talking to the computer with no other company. Somehow, he found himself disconnected from interaction the rest of the universe in that far void, where there was no possible return to the realm of galaxies, and local reality seemed to be disintegrating somehow, as the ship had lost its causal connection with the rest of the universe.

I think there was some sort of connection implied between the computer simulation notion and the disintegrating isolated reality state the character ended up in. I don't know if that necessarily meant that we are in a simulation; it may just have been some more philosophical connection.

I think they may have mentioned never having come across another sapient race in all of humanity's vast expansion, but I'm not sure.

Sorry if this is rather vague; it's about all I can remember of the story, and I may be pulling in some detail or two from another story.

I'm pretty sure I didn't read it in the last few years, which is why I place it in the '00s or earlier, and the computer simulation aspect is what makes me think it was '90s or later. It's possible that I read it in some collection, rather than the aforementioned magazines.

I think this may be "The Cabinet of Oliver Naylor" by Barrington J. Bayley...at least it's reminiscent.

The computer simulation is called the "thespitron" and to modern readers it resembles nothing so much as Star Trek's holodecks. The story even starts out with the protagonist in a film noir detective story like the ones Picard enjoyed.

The spaceships are called 'habitats' and the FTL drive is called the 'velocitator'. The 'velocitator' is capable of stupendous speeds, at the beginning the protagonist is traveling at c¹⁸⁶...

While waiting, he glanced through the window at the speeding galaxies,
then crossed to the velocitator control board and peered at the
speedometer, tapping at the glass-covered dial.

"Will we get there soon, do you think? Is 186 your top speed?"

"We could do nearly 300, if pushed," Naylor said.

......Velocitator speeds were expressed as powers of the velocity of light. Thus 186, Naylor's present speed, indicated the speed of light multiplied by itself 186 times.

The protagonist and his friend do locate and dock with another habitat, and they do have dinner together. (The society is kind of a neo-or-revived-Victorian one). The person from the other habitat does, indeed, slowly reveal himself to be crazy.

The crazy guy uses his 'zom ray' device to push the protagonist's habitat up to such a velocity that his 'velocitator' can't cancel it and the habitat shoots out to the edges of the universe far from any galaxies.

The protagonist gives up and decides to lose himself in the thespitron world.

At the end there is some problem with the thespitron. It ends like this.

Derived of the massy presence of numerous galaxies, the signposts of
reality, the thespitron had ceased to function.

The closing circles were getting smaller. Now there was only the shell
of the habitat, analogue of a skull, and within it his own skull, that
lonely fortress of identity. Naylor sat staring at a blank screen,
wondering how long it would take for the light of self-knowledge to go
out.

The story's quite dense and complicated and I probably haven't explained it well. But if this is it, I am betting you will recognize it at once, it's not like any other story I know.