Philosophy divides the mystery of consciousness into two problems. The Soft Problem is "how does the brain compute things?". The Hard Problem is "how does qualia exist?".
The Soft Problem is easy to imagine. Neuroscience will solve it eventually. We may not understand it yet, but we can make a lot of computer analogies and educated guesses. After all, computers are already Philosophical Zombies (someone who passes the Turing Test, yet in no way experiences qualia).
> but it doesn't lead me to question the nature of reality in any deep philosophical way. Should it?
Here's the contention the professionals are currently debating. The Hard Problem challenges our notions of Physicalism (as opposed to say, Dualism). "But souls are dumb, Science says so!".
Extrapolate into the future. Even after Neuroscience solves the brain's circuitry, qualia will remain just as mysterious as ever. E.g. suppose we discover that the hippocampus demultiplexes memories to different parts of the brain. Suppose we learn how to directly manipulate memory. Not only can we fix amnesia, but we can implant false memories. "Hooray, we've solved the Soft Problem!". But we still have no leads on the Hard Problem. A hippocampus doesn't distinguish a Homunculus from a P-Zombie.
Physicalism has been so successful in the sciences, everyone takes its accuracy for granted. I myself consider Physicalism true. But Physicalism is not adequate to explain the Hard Problem. This doesn't mean we have to go back to souls. But it does mean we need to (at least) "spice up" Physicalism, or maybe choose another line of attack, etc if we're ever to crack the Hard Problem.