I believe consciousness needs some kind of mutable internal state because otherwise literally everything is conscious, which makes the concept useless. A rock "computes" a path to fall when you drop it but I don't believe rocks are conscious. Panpsychism is not a common belief.
I think Nagel put it best in 1974: https://www.philosopher.eu/others-writings/nagel-what-is-it-...
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.