> There is no mechanism for the llm to know the answer to “what are you” other than training data it was fed.

The training data and the system prompt but yes.

I agree there's no reason to believe it's self-aware (or indeed aware at all) but capabilities and origins is probably among the questions they get most, especially as the format is so inviting for anthropomorphizing and those questions are popular starters in real human conversation. It's simply due diligence in interface design to add that task to the optimization. It would be easy to mislead about if the maker wished to do that of course, but it seems plausible that it would usually be have been put truthfully as a service to the user.