They do learn in context, and very sample efficiently. Continual learning is active area of research and we sort of already have something resembling it with persistent context. So yes they do learn.
> Consciousness isn’t really guessing the next thing to say-
I don't know what consciousness is either and these debates are a dumpster fire when they happen, but it sounds like you're pulling forward this "LLMs are just predicting the next token" (true by construction) implies that they can't learn or reason or be conscious (2/3 are wrong, the last one isn't falsifiable without a useful definition).