But humans can do things Turing machines cannot. Such as eating a sandwich.

That's not a computation, it's a side effect. It just depends on what you wire your "computer" up to. A Turing machine in itself is just a (potentially non-returning) mathematical function, but you are free to map any input/output to it.

Actually, the way LLMs are extended with tools is a pretty much the same (an LLM itself has no access to the internet, but if it returns some specific symbols, the external "glue" will do a search and then the LLM is free to use the results)