> Is your arm part of your body?
Of course yes.
> Your hair?
Of course yes.
> A wig?
Of course not.
> A pacemaker?
Depends on who's asking and why.
> A well-fitted mechanical exoskeleton that you use without thinking about it? A poorly-fitted exoskeleton that you're still learning how to use?
Of course not to both of these things.
> A Jeep?
Of course not, and framing a Jeep and a human's liver as if the only possible point of difference between them is whether or not you can "feel" them is strange.
Half of us are fully capable of growing an entire other human being within our bodies, with a physical connection so tightly integrated that breaking it causes bleeding for weeks - and yet it's debatable whether even that counts as being a part of our bodies (especially medically speaking). Navel-gazing about the distinction between your body and a car not being clear-cut is simply inane to me in comparison.