If the question is what is there about us that's not covered by the body, we can mention things like: feelings, intentions, perceptions, acts of consciousness.
Or however else you want to divide up things that have to do with the mind.
Eliminativists/illusionists may completely deny such things. The rest can fall into many camps, some of them religious.
It's not like there are any surprising new parts. It's about how one chooses to interpret/conceive those we are familiar with.
And what part remains in that space after we have mapped all the brain signals and configurations corresponding to these feelings, intentions and perceptions? I don't feel the need to bring up absurd unproven concepts without waiting for more data. It'd be like me saying there is something aphysical behind Mercury's orbital perturbations if I were born before SR and GR were discovered (as an example). No point in jumping to such an argument without first exhausting more believable causes first. History is very strongly against any kind of bet in the aphysical.
My question to you would be, what do you think remains that's not a simple natural system if/after something like Neuralink is successfully established?
Another different question to help me understand what you think of this. I think you agree with me, but just to clarify. A human being is independent of the process of creation right? If we created a molecule by molecule synthesis of a human being, you'd agree it is conscious and the same thing as a human created via typical reproduction, right?