Great exploration!

A thought : maybe the poem prompt kind of contaminated and fostered the use of “I” by asking “about being an AI”; key word “being” naturally implying that it is an self-aware “I” who is.

Admittedly, the poem could have been written in the third person; but as the topic of the third person was mentioned earlier in the conversation, the AI might have guessed it worthy of being explored in the poem.

I don’t know if this thought has any value to the argument of this post, other than to say that indeed, AI is good at making us believe things, because we like patterns and AI is a good pattern wizard pulling rabbits from hats we can barely fathom.