Essentially, something is conscious iff "there is something that it is like to be" that thing. Some people find that completely unsatisfying, some people think it's an insight of utter genius. I'm more in the latter camp.
Also, I think consciousness is non-binary. Something could be semi-conscious, or more or less conscious than something else.
Anyway, I don't think that there's anything that it's like to be an LLM. I don't see how anybody who knows how they actually work could think that.