Activating organs using the brain

What actually makes it part of the body? The connection itself?
And if the hand is simply connected using some special holder and the control is done entirely by a chip that transmits waves that create the communication, meaning there is no physical connection of electrical wires to the body/brain/chip.

What would be the difference between this and a wheelchair that has a connection like a kind of tube from the head to its operating mechanism.

I'm talking a little science fiction.
On the other hand, the sages talked about a flying box, so I think I'm in good company

This is not science fiction. The poskim have dealt extensively with cochlear implants in the ear and even glasses (in the matter of wearing them on Shabbat), which they see as part of the body. This is not related to the question of how the Libor is made, but rather to functional functioning.

It sounds logical to follow the rules of expenditure.

But, is there no difference between a cochlear implant and glasses, whose use is passive (the implant is activated before Shabbat) compared to a hand, which is active?

And perhaps it is problematic in this case to follow the rules of expenditure. For example, an electric/digital watch is permissible to carry around as long as it is not used beyond its passive use.

And another question on the same weight, why actually ban an electric wheelchair, whose function is essentially to replace the legs? (Not talking about the electric vehicle in the change of ‘intersection’).

I didn't say to follow rules of expenditure. I brought them up as an example of this type of consideration. It is not intended to claim that everything will be determined by rules of expenditure, since I have not tested this thesis (on its face it seems quite reasonable).
Whether the function is active or passive really doesn't matter. Our natural hand is also an active function and we are allowed to send it electrical commands from the brain to operate it. An electric wheelchair is similar but not quite. It does not function as a limb but replaces it with something else, and this other something is also operated like a device with switches and presses and not from our brain. That might be worth discussing.