Pretty much total, if the admin or admins want to exercise it.
It's on their hardware (literally or figuratively), and they're responsible for what happens on their instance (up to a point).
However, that's not all instances, at least not in a practical sense. I can't remember which ones are which, but some of them are set up where no single person can engage in fuckery without being checked. Yeah, at some point someone could pull a literal plug, or otherwise flip the table on that, but it isn't going to be easy.
The good thing is that it doesn't matter. I'm on sh.itjust.works. If it folds today, with no warning, all I lose is my user history. Even that, it's really only the ones thaw are only on this instance. The stuff on other ones is still there, I just can't do anything with it.
But I could, if I hadn't already, just sign up on another one, and by way of being a prolific bastard, not skip a beat. Since I regularly export my info, subscriptions and blocks and such (I can't recall what all does and doesn't get transferred), I can just import that to wherever, and it really isn't noticeable on my end.
However, it's on me if in not backing up my comments that I feel have value. Same as on any platform, there's no guarantee of tomorrow. You always back up anything you want to keep that isn't already on your own hardware. My two accounts under my pen name, I copy/paste everything I write into a notepad and back up those files.
Of equal import is that once a given instance goes too crazy, it's likely to get defederated. So one that goes deep into censorship won't be a major problem for long, and that's been the case a few times.