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In the last episode of Game of Thrones (season 8, episode 5)

Daenerys executed her master spy, Lord Varys, for treason by burning him alive.

I do understand that he was favouring

Jon Snow

to be the king of the Seven Kingdoms because he thought that he would make a better ruler than Daenerys. Plus, he said several times during the show that

for him it doesn't matter who sits on the Iron Throne, because he fights for the people, so he will favour whoever he sees will be the best ruler for the people.

However, other than the obvious fact that was prompting

Jon Snow

to take the crown (in a private conversation, which never arrived to Daenerys because she had shut herself in the castle), I saw no actual treason that would justify his sentence.

From what I understood he just “knew the truth about the heir to the Iron Throne” the same as Tyrion did (and basically half the main characters of the show thanks to Sansa).

So was there a formal accusation held against him for his sentence, or was he executed just because Daenerys wanted to do so?

He was executed for treason, the main reason appears to be because he was conspiring outside of Dany's orders to inform everyone who Jon Snow is and that he has a better claim to the Iron Throne and so should sit on it instead of her.

Tyrion: Your Grace? There's something you need to know.

Daenerys: Someone has betrayed me.

Tyrion: Yes.

Daenerys: Jon Snow.

Tyrion: Varys.

[...]

Tyrion: If I have failed you, my queen, forgive me. Our intentions were good. We wanted what you want. A better world, all of us. Varys as much as anyone.

Daenerys: But it doesn't matter now.

Tyrion: No. It doesn't matter now.

_{Game of Thrones, Season 8 Episode 5, "The Bells"}

Note though that Tyrion is aware that Varys would also try to assassinate Dany following their conversation in the previous episode so could have told her that off screen.

Varys: You know where my loyalty stands. You know I will never betray the realm.

Tyrion: What is the realm? A vast continent, home to millions of people, most of whom don't care who sits on the Iron Throne.

Varys: Millions of people, many of whom will die if the wrong person sits on that throne. We don't know their names, but they're just as real as you and I. They deserve to live. They deserve food for their children. I will act in their interest, no matter the personal cost.

Tyrion: So, what happens to her? Please. Don't.

Varys: I've spoken as honestly as I can. Each of us has a choice to make. I pray we choose wisely.

_{Game of Thrones, Season 8 Episode 4, "The Last of the Starks"}

In "The Bells" it also appears that Varys is trying to poison her through the use of Martha bringing her food. However, Dany seems to be somewhat wise to an attempt to kill her and has locked herself away and isn't eating.

Varys: And? Nothing?

Martha: She won't eat.

Varys: We'll try again at supper.

Martha: I think they're watching me.

Varys: Who?

Martha: Her soldiers.

Varys: Of course they are. That's their job. What have I told you, Martha?

Martha: The greater the risk, the greater the reward.

Varys: Go on. They'll be missing you in the kitchen.

_{Game of Thrones, Season 8 Episode 5, "The Bells"}

It’s also worth noting as mentioned in a comment that Dany made Varys promise to tell her to her face instead of going behind her back if he ever thought she was in the wrong. Whilst he has done that initially she ignored his advice and so now he’s going behind her back against her wishes so that probably plays a part in it too.