LLM are definitely not sentient. As someone with a PhD in this domain, I attribute the 'magic' to large scale statistical knowledge assimilation by the models - and reproduction to prompts which closely match the inputs' sentence embedding. GPT-3 is known to fail in many circumstances which would otherwise be commonplace logic. (I remember seeing how addition of two small numbers yielded results - but larger numbers…
In the book professor Robin Dempsey almost become mad by chatting with ELIZA and gradually begin to believe it's sentient to the point of being ridiculous.
PS: Apparently it was also adapted in a British TV serie in 1988, but unfortunately at that time they tended to reuse magnetic band and it's improbable that we can dig a clip out of that. Would have been appropriate an illustration!