Badenov
SOC-13
This sounds like a familiar background story, but it doesn't address the idea that psions also get the propaganda and know that being caught will get them put away. It's super-easy to not use powers that will get you put away if you use them, it's not like you can accidentally use psionics or be compelled to use it against your will. That leaves only the few psions who can't resist using their powers to get caught. Obviously you'd have psionic agents at every school listening to see who's listening in to others' thoughts, but even school kids are smart enough not to do stuff that will get them dragged off. At least most kids. And the only ones who grow up and have kids of their own are the ones who can keep their powers secret, and they'd tell their kids so the kids wouldn't get dragged off.I'd see it handled more by propaganda if psionics were known but the government wanted them suppressed. You have a sustained campaign that spreads propaganda about how "dangerous" psionics are. You instill a fear and loathing of them in the public. Over time, someone who displays psionic powers ends up being reported to the authorities by witnesses who have been indoctrinated to do just that.
You only need the nobility empire-wide to order and sign onto such a campaign. Now, they might be in the know about any psionic that is arrested being sent to a government facility for training as an agent or something, the central government even possibly giving out a suitable reward for their cooperation in catching the psionic. That would incentivize the ruling powers to find and arrest such persons.
For the public, they just know psionics are dangerous and if you are able to report one and it's confirmed, you get a good reward for it. That would make for a great policy polity wide.
Make it something like the agency in the show Dirk Gently's Holistic Detective Agency.
Also, how obvious are psi powers? In movies, there's a special sound effect surrounding the use for the benefit of the slower audience members, but RL comes without SFX (unless there's some IYTU - that would make things super interesting in a very different way) and you wind up with a guy who wins at roulette ten spins in a row with no outward signs. But that's one out of every thousand or so players anyway, so that's hardly a smoking gun.
Obviously some powers are more subtle than others, but I would expect in a psionic-restricted society as described, there's 10 or 100 times as many psions who play it cool and don't get caught, many raised by parents who gave them The Talk at an early age.
So I want to caveat all this with me not knowing how psi powers work in game, I'm thinking about general cases. If there's a Detect Psi power, it's all over, of course.