The Chomsky hierarchy is a classification of grammars. So it's about Syntax.

GPT is purely about semantics, about truth. To the extent that I think it can be said to be fundamentally informal in its dedication to truth, since it can easily be prompted to produce syntactically incorrect output - wrt the syntax of whatever language whose semantics determine the truth GPT is asked to reflect.

So I think this is a categorically incorrect question.

I mean, what is the fundamental syntax of the output of an LLM? It would have to be that any sequence of utf8 chars is valid.