> Has an AI agent ever woken itself up without a prompt and run a forward pass towards some goal, aligned or misaligned?

Yes, I think people do experiment with continuously running AI, e.g.

https://www.reddit.com/r/LLMDevs/comments/1sblzbe/what_i_lea...

It's not a common thing to want though. Much nicer if we control the prompts.

> To me, it’s beyond odd we call these thing agents without acknowledging the clear differences in the dynamics of their behavior.

They're called agents because they can act on our behalf. Which they do.