It's actually not hardware at all. I say this not to be annoying but to make the point that perhaps we shouldn't be computer-morphizing the human brain. (I know that's not a word but was the best I could do!)
I agree with not "computer-morphizing" the brain, but I think hardware still applies well enough. Is there a specific reason you think it doesn't apply out of curiosity? I mean, are you just trying to avoid the "duality of hardware and software"?
It is a substrate. Not quite the same as hardware but close enough for government work.
technomorphizing maybe? it's definitely something we do.