This is a bit of extrapolation but I would say the reason why we’ve been unable to locate “consciousness” in the brain is because it’s the same thing. Relatively simple neurones, chained together, to create thought.
On a philosophical level: this doesn’t make any claims for idealism or materialism, “experience” could exist at a more fundamental level of reality than matter. But IMO that would mean that the LLM is “experiencing” as well.