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?
It's not necessary to incorporate metagaming into Paranoia, you shouldn't have any problems running it more conventionally. Those suggestions are pretty much just for fun, and if you don't think they'd be fun for your table, don't do them. I think the reason it suggests things like punishing a PC for OOC questions is to set the tone of, well, paranoia. Poking around at things you don't need to know is always risky. Also, I wouldn't say backstabbing is necessary either. If the players would rather work as a team, let them, give them NPCs in case they do need to backstab somebody.
However:
This is the only part might be a problem, lol. Paranoia is all about rules lawyering. A big theme of the game is coming up with convoluted technicalities, either to hit your players with, or for players to justify their actions, or for players to pass blame onto other players with. Like, the computer instructed you to do this task, and obviously you have to do X to accomplish that task, but you don't have the clearance to do X, and the computer won't explicitly give you permission or provide an alternative (realistic) solution, so the challenge is finding a way to get X done while having plausible deniability or being able to blame someone else for it.
A lot of the ideas behind the system are to turn assumptions about roleplaying on their head and to give permission (and encouragement!) for things like (in character) rules lawyering. Idk if that sounds bad but like it's a satirical setting where nonsensical, contradictory rules that make it impossible to do your job are played up to 11 for comedy and as long as you're following the exact letter of what you're told, anyone who challenges you or interferes in any way is committing an act of treason and trying to get you to disobey orders because they think they know better than Computer, and is probably also a mutant commie terrorist. The more bizarre technicalities and loopholes your players come up with to get away with shit ("getting away with shit" here also including, actually doing their jobs without dying), the more immersive the setting. It's cathartic.
It's a rules-lite system that's flexible enough to fit a lot of different styles, but in my personal opinion, that sort of rules lawyering and malicious compliance is what makes Paranoia Paranoia. If none of that sounds appealing, you could still probably make it work, but there might be another system that's a better fit.