I'm interested in starting a game of Paranoia for some friends. This would be the latest edition. I've never run this game before, and I see plenty of online discourse about how to stoke intrigue and backstabbing betteen PCs. What has confused me when reading about the game (Core book, but also online comments) is how the GM is encouraged to mix in-game and out-of-game actions/consequences. Eg: In the rulebook, it gives an example of the GM removing XP from a PC because their player IRL asked a question that in-game would be considered treason. Opposite examples would be when a PC has to fill out a crazy requisition form to get their equipment, so the GM prints out a sheet and makes the player fill it out under a time constraint.
I've always enjoyed games where the skills/knowledge of players IRL is not reflected in-game. I always felt that if your character is a world-class orator, then the ability of a player to RP that oration should be inconsequential (except for fun, obviously) to what happens in the game.
I would consider my players trustworthy. I can be reasonably sure they're more interested in a good story than rules lawyering or metagaming. Can I run a Paranoia game according to these principles, or should I look at another system?
You need to talk to your players about this. Explain the kind of stuff that can happen in Paranoia, and ask them if they're down for those shenanigans. Ask them what kind of stuff they don't want to do - maybe someone really hates paperwork, so that would ruin their fun, but they're cool with everything else.
This kind of pre-game agreement is called Session Zero. Searching for it should give you some ideas on how to prepare for it.