That's not the point. Computer program with a finite number of steps (an auto regressive LLM without chain of thought) has a limit in what it can reason in one step. This article does a lot of wordcelling to show this obvious point.
That seems irrelevant to Gödel? If that was your point, you should have said that rather than the things about Turing and Gödel (which leads people to expect you are talking about the halting problem and incompleteness, not the limitations that come from a limited depth circuit)