All right, let's tackle it a bit more directly than replacement: Does amputation of a limb diminish an individual's personhood? Is your answer dependent on the use of a prosthetic?
I mean, I saw this guy who had both legs amputated. He entered the Utah Summer Games in the 100 meters in the "open" class, meaning he was taking on the best in the state straight up - no "handicapped" class. He took first in the preliminaries and second in the final.
If he thinks of himself as an athlete, he still is. But if he wants to play footsie under the table with his SO... that's something he lost.
So it depends to some degree on where your sense of personhood is. But I think for all of us, we're not a brain in a vat. We interact with our external physical environment. If you lose all of that... haven't you lost something that matters to you? If you can't enjoy a steak, can't enjoy a kiss, and can't enjoy the smell of a flower (or even the sight of one), then aren't you something less than you were when you could do all those things?
In fairness, the context was uploading the brain, and whether the whole body was needed, so it was a semi-reasonable misread.
Still... there's a large distance from "I can have a heart transplant and still be considered the same person (even though 1% of my body now has different DNA)" to "I can have no body at all and still be the same person". The claim was that a body is a significant part of who we are as people, which is not a claim that a heart transplant addresses at all.