Our whole nervous system is a big neural network that extends through the entire body. There’s additional networks at each of our organs and muscle groups. They are already known to contribute to finer control of the organs, eg the brain doesn’t need to send signals to each individual heart muscle for each beat, the heart’s “brain” can handle that on its own. Reflexes and muscle memory can be handled more locally, too. Same with stress level, your liver might decide you’re irritable because of all the alcohol it needs to process.

But at the end of the day, it’s just a massive self-learning neural net that can encode other things. If you play a music instrument, maybe your finger neurons store more of the memory of how to play specific songs than you’d expect. So if you’re an expert piano player and lose your hands but replace them with prosthetics that can easily outperform normal hands, you might not be able to play the songs you could expertly do before. Hell, maybe even foot tapping along with a beat means that part of the experience in hearing or remembering some or all songs involves neurons in your legs.

You’d still feel like you, but parts would be missing. It’s not very well understood to what extent, but it does look like there is an extent, and not just for the gut “brain”.

I mean, there was that one guy where the mob cut off his entire body