And how do you know LLMs can't tell that they are involved in a conversation?
Unless you think there is something non-computational in the human brain, then you must accept that computers are - in theory - capable of thinking. With the right software and sufficiently powerful hardware.
Given that truth (which I think you can only avoid through religion or quantum quackery), you can't just say "it's only maths; it can't be thinking" because we know that maths can think.
Do LLMs "think"? The definition of "think" is wooly enough and we understand them little enough that it's quite an assertion to say that they definitely don't.