>Basic information theory tells us that any noisy continuous system is equivalent to a discrete system of a certain resolution/bit-depth.

Not only that, but the https://en.wikipedia.org/wiki/Bekenstein_bound also tells us that in a finite region of space with finite energy, there's a fixed bound on its information content. So if the brain exists in finite region of space with finite energy, then it can be described without loss of accuracy by a discrete system.