The human brain is not that different. Our long-term memories are stored separately from our executive function (prefrontal cortex), and specialist brain functions such as the hippocampus serve to route, store, and retrieve those long term memories to support executive function. Much of the PFC can only retain working memory briefly without intermediate memory systems to support it.
If you squint a bit, the structure starts looking like it has some similarities to what's being engineered now in LLM systems.
Focusing on whether the model's weights change is myopic. The question is: does the system learn and adapt? And ICL is showing us that it can; these are not the stateless systems of two years ago, nor is it the simplistic approach of "feeding old context back to it."