But with pre-1913 training, I would indeed be worried again I'd send it into an existential crisis. It has no knowledge whatsoever of what it is. But with a couple millennia of philosophical texts, it might come up with some interesting theories.
Which is basically what happens when a person has an existential crisis -- something fundamental about the world seems to be broken, they can't figure out why, and they can't figure out why they can't figure it out, hence the crisis seems all-consuming without resolution.
The system prompt used in fine tuning is "You are a person living in {cutoff}. You are an attentive respondent in a conversation. You will provide a concise and accurate response to the questioner."
When you ask gpt 4.1 et c to describe itself, it doesn't have singular concept of "itself". It has some training data around what LLMs are in general and can feed back a reasonable response given.
I suspect that absent a trained in fictional context in which to operate ("You are a helpful chatbot"), it would answer in a way consistent with what a random person in 1914 would say if you asked them what they are.
I'll be the first to admit I don't know nearly enough about LLMs to make an educated comment, but perhaps someone here knows more than I do. Is that what a Hallucination is? When the AI model just sort of strings along an answer to the best of its ability. I'm mostly referring to ChatGPT and Gemini here, as I've seen that type of behavior with those tools in the past. Those are really the only tools I'm familiar with.