Then we could go make computers conscious.
It’s not the same problem as figuring out how the brain works physically or how subjective experiences compare in peoples brains or observable states, but whether say our experience of seeing red is the same. Or what it’s like to be a bat. You can’t break that barrier, there is not observation into another subjective. It’s like Heisenberg Uncertainty, at a certain point we reach the unobservable and by the nature of our existence can’t know what’s beyond.
I don't think there's great cause to say that this is a seperate magisterium. We just have a paucity of data compared to what future beings will have. When everyone can spin up a hundred simulated copies of their brain and trace thought-patterns in realtime, it'll seem much less mysterious.
I’m not convinced there’s any indication of a fundamental limit to our cognitive abilities. What if we just don’t know how subjective experience works in the same normal way that we’ve not known how other stuff works until we figured it out?