My understanding is that the brain, to the extent that it is a computer, is not anywhere near Turing complete. It is not something more than a very fast (Turing complete) computer, it is something less. The brain makes up for the deficiency by being extremely fast and well optimized for the tasks it needs to do.

But as a consequence, we cannot draw the metaphor about the brain being a "computer" too far. The "software" in the brain is specific to the given brain, and not hardware independent.

Sure, if we imagine a Turing machine with infinite speed and memory, it might be able to run the "software" from every human brain, but we do not know if it is even possible to build such a computer within our current universe (if we require it to operate at real time). And if it is possible, I would guess that it would be so many orders of magnitude less efficient than a non-Turing complete machine that there would be little reason to build it.

Penrose and others try to smuggle in something like dualism through QM, but I don't see why that is necessary at all.

I think we just need to throw out most of the "Computer" metaphor that requires Turing completeness, and deal with the brain for what it is.