It's worth keeping in mind the model doesn't keep a running memory. Each time its instantiated, it begins from its release state - so from its perspective (if it had one) the current task would be the first stop after posttraining. Perhaps the only stop.

Though of course you're talking about data centers, and romanticizing them rather than the AI itself.

No, llm providers will start providing a service that looks a lot like rumination or (day)dreaming. Like thats the prompt "you're daydreaming about this work you recently did" then add in whatever is in the current session.