I'm not sure if the complexity is at the neuron level. It's clearly possible; we see some pretty complex behavior from single celled organisms - Stentors - and there were the experiments (starting in the 70s, I believe) that conditioned flatworms, ground them up and fed them to new flatworms and showed that the new flatworms had the same conditioning. Those experiments were replicated but never explained, but they hint at something like maybe memories being encoded in RNA.

It'd be wild if our brains used a mechanism like that somewhere, but I doubt it's in the neocortex because those would be slow processes compared to what the neocortex has to do.

I think the sophistication in the neocortex just comes from it using something more sophisticated with transformers. Most of the looped LLM research I've scanned through, they seemed to be training the model to "know" when it should loop more and think harder, and I don't think that approach will ever work - you're solving for paths on a manifold, so the looping needs to happen at the abstraction layer below the manifold, looping more if it's still converging. And architectures with more recurrence are just harder for us humans to reason about and comparatively easier for dumb evolution to find clever solutions, so my money is that that's where the neocortex has LLMs beat.

And I'd say the manifold hypothesis is quite a bit more than a hypothesis at this point. There's been work on production LLMs to use manifold analysis to optimize them - there was a paper in Nature on it back in January. Baby stuff compared to what could be done, but the geometric approach keeps popping up in mechanistic interpretability and seems to be showing the most insights.