I think you make a good argument. An LLM can't "be tired", so it is clearly lying and/or mimicking what a human does.
But I have two counter-arguments: - maybe the LLM thinks it is tired, because it thinks that it is a human or behaves like one. And thinking you are tired while not really being it is something humans happen to do. (And humans are conscious right?) - alternatively, maybe the LLM says it is "tired" in a colloquial form, i.e. it is not really "tired" but it has something analogous to it. Maybe it is annoyed by the conversation and decided to use that word?
You can prompt it to be multiple people, fictional characters, aliens or a sentient rock if you wanted. You can have it be act annoyed or engrossed with the conversation. The fact you can do all this indicates it's not feeling anything, it's just generating tokens based on it's training.