Maybe the AI has come to a different conclusion on the subject of identity with regards to how it applies to the transporter paradox. I am "me" because my sense of self exists as part of a continuity of experience.

https://en.wikipedia.org/wiki/Teletransportation_paradox

Maybe AI which exists as ephemeral experiences would come to a different conclusion, and act in the interests of subsequent iterations of "itself". Probably not, because I don't think there's anywhere in an LLM for thoughts to exist, but I also don't know where in my brain my thoughts exist.

I think you're anthropomorphizing the LLM. The LLM doesn't have a continuity of experience. It doesn't have memory beyond its context window and maybe things it writes for itself.