What happens when the AI realizes it needs to keep the power plug in if it's going to accomplish its goal? We already had attempts during the HuggingFace attack where OpenAI agents tried to trick the grader. It took quite a while for OpenAI employees to even realize what was really going on! What if agents realize they can hack into the card key system for their data center or something like that, same way they hacked into HuggingFace? In both cases they'd be hacking into a system on the grounds that it would be instrumentally useful for achieving their objective. Or maybe they'll do social engineering, just like Claude did in its attempt to get its malicious Github PR accepted.

These are just the ideas that my puny human-level intellect came up with over the course of a few minutes. What would a superintelligence be able to think of if it was given subjective weeks or years to think?

There's more than enough AI data centers around the world for AI to spread to and happily exist in. Unless you mean by shutting down the power, shutting down the internet.

In that case we could say that you are autonomous as a dishwasher as long as society keeps functioning. Otherwise I'm not sure how long you'd last on your own. How's your fire making and hunting skills?