[YeGoblynQueenne]

Your turn of phrase "there's no AI getting stuck..." has me stuck. Are you assuming that there exist "AIs", as in artificially intelligent entities, like the kind imagined by science fiction writers and (some) AI researchers, alike? To clarify, there are no such systems. "AI" is the name of a research field, not any ability that characterises a class of systems currently known.

This suffices to explain why there is, indeed "no AI getting stuck inot a loop by a tricky question". Because there is "no AI" at all, certainly not of the kind that can understand a "tricky question" sufficiently well to stumble on the paradox inside it.

For example, GPT-3 has no ability to process "this sentence is false" in such a way as to decide its truth. AlphaGo is not capable of processing language at all, it is only capable of playing board games and it isn't even capable of playing board games by reasoning, only by search. AlphaGo searches a game tree structured as a directed graph, without loops so it's hard to see how it could get stuck on recursive paradoxes anyway.

In general, such systems as exist today do not have the mathematical properties of the formal systems described by Gödel, Church and Turing. They don't even have memories. So they are, let's say immune to incompleteness, because they're not even incomplete.