I don't think any frontier lab tried to make an LLM optimized for the literal Turing test where the LLM is made to argue that it's human. This is not in their interest. They make their LLMs insist they aren't human, have no feelings and sentience etc etc.
So we don't actually know how good LLMs can be in this.
So we don't actually know how good LLMs can be in this.