Bizarro responses. The "usually means" is what people IN kindergarten (or rather those at that level of maturity) mean by category mistake, it's not what informed intellectually honest people mean by it. It seems clear that my correspondent has no idea what it means and is simply lashing out.

It's a category mistake because thinking like we do requires a certain sort of algorithm or one operationally equivalent to it, whereas things that are Turing-complete include Befunge-98 and C++ templates. While something being Turing-complete implies that the cognitive algorithm could be implemented with it, clearly the categories are incorrect.

Note that, while the set of all LLMs with CoT covers Turing completeness, a specific LLM with CoT is only Turing-complete if it has the right weights, but training does not produce such LLMs. Note also that there are no UTMs in the real world since that requires unbounded resources. This is true all digital computers and well as brains so is not a fatal blow to LLMs, but the resource limitations play out very differently in LLMs and brains.

As for the dead troll comment, not only is it a foolish ad hominem on its face, it's quite false -- I'm an atheist and do not believe in souls.