You're right, this is a very difficult question to answer, and I don't have a clear answer for myself either.
My intuition here is that ANY private citizen acting without authority derived from a due process, or the necessary clearance, is breaking the law and needs to be arrested. Full stop. It bewilders me that Musk wasn't apprehended before he was given special permission to do what he was doing. This was blatant evasion of democracy and potentially harmful to hundreds of millions of people, and harmful to democracy itself. It sets an incredible precedent.
The check or balance that appears to be missing, I suppose, is the one where people feel they have the agency or ability at all to identify this type of nefarious behaviour and report it to an entity which can act to rectify it, independently of the president. Trump has enabled this every step of the way, and ultimately, any attempt to fix this likely would have been defused by him as well.
I'm not sure what citizens can do, or how exactly the institution should protect itself in the future. But there are many historical parallels to what's happening here, and inaction on citizens' parts is certainly a large component. Too many people are failing to stand in the way. Part of the solution is making it possible to do so. They step aside because the consequences, especially in the USA (with leaders who blatantly seek to purge their opposition), are far too great for an individual to absorb.