Conversely, ChatGPT does decently well on multi-armed bandit tasks, demonstrating (rudimentary) reinforcement learning capability during inference. It's known that LLMs evolve their own optimizers in the process of acquiring few-shot learning, so I assume it picked up these RL abilities similarly. That kind of on-line RL is foundational to autonomous agents.
The prompt isn't part of the LLM, it's part of how the LLM is wired into a chat window. You can make them stream tokens forever, or prompt themselves, or ditch causality entirely. The foundational abilities for autonomy, I think, are in there, for the simple reason that they've learned to model autonomous agents - human beings.