Wouldn’t he have to get on the ballot in all the swing states at least? What if some states refuse to let him run? I can’t see California registering him for example, but that wouldn’t really matter of course.
Only if he tries to get a 3rd term by a fair election. The more realistic way to it happening is by hijacking the electoral process. There are a number of ways to do this, such as by claiming there was fraud and thereby having the justification to modify how "electors" [0] should cast their vote. This is exactly what was tried in the 2020 election.
Really, it's just an "if enough people in power and in general go along with it, then it works" kind of thing. The current trend in the GOP is to whip and/or expel those who do not fully support Trump. What happens if half of the elected politicians, most of their constituents, and most of the appointed government officials, decide that Trump is staying in office? No one knows. The power of words on paper only goes as far as people let it.