People get into philosophical trouble with this because humans have a hard-wired system for what's part of your body and what isn't. That's a survival trait. Problems with that system cause phantom limb syndrome, self-injury, and other body-model disorders.[1]

We're looking at a protection system from the inside. Brains are internally interconnected distributed systems, but we're evolved not to feel that way. Trying to reconcile that drives philosophers and theologians into inventing dualism, souls, and other hacks to explain the concept of a unified mind. That goes back at least two millennia and hasn't helped much.

Brains are distributed systems. They have features to drive them towards eventual internal consistency. Failures of those features underlay schizophrenia and similar disorders. Has neuroscience explored eventually-consistent system theory yet? That might be useful.

[1] https://wolpertlab.neuroscience.columbia.edu/sites/default/f...