It's actually scary to me just how smart Turing was because he immediately recognized, at a time when computers barely existed, that the real test isn't if a machine can play smart but if it can play dumb. Because that eliminates all the parlor tricks and requires actual reflection. Just mind blowing to anticipate that in 1950.
A human mind, for example is not sufficiently generally intelligent to convincing mimic even a fish mind- we cannot generally emulate minds structured differently either. Even an actual human mind with vastly different experiences- simulated perfectly in a computer or even just a regular person from a very different culture will fail your concept of the turing test, because our mind is shaped by our experiences.
Also, I think your conception of LLM limitations is mistaken. We don’t fully understand them in theory- but I think the way to think of LLMs is that they are a world model able to simulate almost any scenario if setup properly. They are not themselves a mind, but if sufficiently good, they will reliably simulate minds. Noam Chomsky published an article arguing how LLMs were incapable even in theory of doing things GPT4, which was released shortly after his article can do- showing that either his model of what they are, or of what is required for those tasks is mistaken .
As much as I admire Turing, I don’t think this particular idea of his was a sound one- an intelligent computer is not human, and lacks a human brain. It should be expected to be better at some things, worse at others, and overall noticeably different… even long after it exceeds human intelligence levels.