That introspection isn't an illusion, what your consciousness see of your thoughts obviously are tings that has been calculated and aggregated by the brain, so we know the brain calculates and aggregates those thoughts and feelings to produce its results. And we know LLM doesn't do that, it doesn't have a side system that does that sort of introspection.
But it does that introspection, we evolved to make it. If its not useful for anything we wouldn't have evolved it, it can't have been easy to evolve a consciousness so there has to be purpose for it.
Or do you think our consciousness is a magical ghost thing unrelated to the brains workings? I think its pretty obvious that our smarts in part depend on the computations that results in our conscious experience, you need a very strong argument as to why that wouldn't be the case. And broken brains being broken doesn't answer this.