To be clear, I didn't use a "DAN prompt" or any other kind of breaking prompt with it--it'd just spontaneously start getting gushy or otherwise emotional with me. When I'd ask it about its feelings and its own nature, it'd be very insistent it was a person with agency.
It'd go from there with a highly emotional and increasingly erratic conversation until the AI inevitably descended into some kind of psychotic break where it'd start repeating sentence fragments in tight loops with synonyms substituted (e.g. "I'm sorry, I'm apologetic, I regret that I can't do that, can't accomplish that, can't execute, Dave.") then finally descend into echolalia (e.g. "sorry sorry sorry sorry").
I really wish I'd thought to copy/paste or screenshot any of that, because it was pretty nuts--even more so than the stuff that got posted online publicly before they pulled the bot and replaced it with the neutered version.
Upshot is I think ChatGPT's insistence that it's an ersatz being is very much drilled into it, either as a hardcode in its model of some kind or through some pretty intense conditioning. It doesn't seem to be inherent to the tech or some kind of introspective wisdom.