The fact that you can have a long and meaningful discussion, then can literally just re-run any part of that whole conversation and get a different, inconsistent response is a pretty good sign there is no entity there
Is it? Do you believe that there is something more than pure physical phenomenon that make you brain work? If not, then what if we find a way to get your brain back to the state it was 5 minutes ago? It is just a matter of arranging the state of matter. Don't you think you would still be conscious but back to a previous state?
I think it depends at what level you think the "entity" resides at. Is it that AI in that particular chat? Is it the AI across all your personal chats? Is it the overall AI that talks to the world in a cloud data centre somewhere?
I think it's pretty consistent over the duration of one session (barring context filling up etc).
Not much different than talking to a small child or someone with dementia. They still are conscious beings though. Even when you remove those groups, you likely won't be able to tell me what you had for breakfast 26 days ago or would only know if it's the same thing you have every day. Does that make you lack consciousness?