A thought experiment: One by one your neurons are replaced by their digital counterpart as a nano-scale computer in-place, with equivalent functionality. After which neuron number are you no longer you? You remain conscious throughout the process, the process may last however long with pauses for sleep. After the replacement is complete, one by one these neurons are switched off with their functionality offloaded to…
Another thought experiment: One by one your neurons are replaced by water. At which neuron are you no longer you? The fact that there is no clear time to pinpoint for a change doesn't imply that there is no such change... so your thought experiment doesn't really prove that the 'you' is kept. In the end, Theseus ship is, and is not, the original ship, and both things can be true at the same time.
You have described an aspect of ageing & decline.
> doesn't imply that there is no such change
I made no such assertion, obviously something is changing. The question is whether or not that change matters to your core identity. The thought experiment in my opinion shows that as long as continuity is maintained and as long as you are happy with the results you remain yourself and gained something in the process.