So back to the questions of "What is knowing?" "Are talking like someone with theory of mind and having a theory of mind the same thing?"
If your argument is that the only way to answer this it to have a first person experience of that consciousness then that's not a scientific question. No one will ever have one for an LLM or any other AI. It's like asking "What's happening right now outside of the observable universe?". If it can't impact us, it's irrelevant to science. If that ever changes it will become relevant, but until then it's not a scientific question. Similarly no person can ever have a first person experience of the consciousness of an LLM, so anything that requires being the LLM isn't relevant.
So that means the only relevant question is what distinction can outside observers make between an agent talking like a theory of mind and having a theory of mind. And given a high enough accuracy / fidelity of responses I think we're only forced to conclude one of two things: 1. Something that is able to simulate having a theory of mind sufficiently well does actually have a theory of mind. OR 2. I am the only person on the planet with a theory of mind, and all of you are all just simulating having but don't actually have one.
It's all "Searle's Chinese room" and "What consciousness is" discussions all over again. And from a scientific point of you either you get into the "it must be implemented identically as me to count" (which is as wrong as saying an object must flap its wings to fly), or you have to conclude the room plus the person combined are knowledgeable and conscious.