Did Descartes choose his wording as a cheeky nod to the name of God? If God is real, then did Descartes have a choice not to make this nod? I like to think it's a joke from on high. A reference to His word in Romans 1, that the thought of any being necessitates the "I am" of Yahweh.
I want to spend a second here due to the emergence of LLMs and the fears surrounding AGI. "Am"ness does not translate to "dignity". For me, "I" think, therefore "I" am. The only actor I can certainly make a statement for is myself. However, I accept extrapolation as an axiom of logic. The AI is thinking, therefore it is. My cat thinks, therefore it is. A rock does not think (as far as I know), but it is. Does an atom think? Maybe. Zoom back a bit again, but to the human cell. The cell is effectively an independent "being". An "am". Does it think? I go through this not to say it is profound, but rather the opposite. "Am"ness is common and prerequisite for conversation. If I were a brain in a vat, I still "am" and must reason with my "am"ness.