Right, the mind processes it, and in turn does something, analogous to how computers process signals, and in turn do something.
Consciousness and computation are entirely up to what we define these words to mean. At some point we have to settle on a satisfactory definition of consciousness that fully differentiates it from computation, or they’re left with at least some overlapping (analogous) meaning.
If we dismiss consciousness as currently unknowable us, and thus undefinable (as your statement about dimensions alludes to), then how can we say assume with certainty, that we haven’t already achieved conscious AI?