It’s never been tested, so it is an open question. Not many people would be bold enough to try, and I don’t think Trump actually will either, but eventually this will go to the Supreme court.

The main problem is, at the time the 22nd was written, there were plenty of cases of presidents who weren’t elected to the office, so why would the text specify only the electoral pathway if it were meant to cover all possible pathways? Even in the most broad reading (no elected official can become president after having been elected president twice), there remain appointed positions within the line of succession - namely secretary of state - that would completely avoid the election clause.

I agree with you that the intent of the 22nd was to ensure a 2 term limit. Unfortunately the language is not that definitive and the current administration has little concern for following the unwritten rules.