An LLM context is a pretty well extended short term memory, and the trained network is a very nice comprehensive long term memory, but due to the way we currently train these networks, an LLM is just fundamentally not able to "move" these experiences to long term, like a human brain does (through sleep, among others).
Once we can teach a machine to experience something once, and remember it (preferably on a local model, because you wouldn't want a global memory to remember your information), we just cannot solve this problem.
I think this is probably the most interesting field of research right now. Actually understanding in depth how the brain learns, and figuring out a way to build a model that implements this. Because right now, with backtracking and weight adjustments, I just can't see us getting there.