> I have not heard of a city moving between continents however.

Continents are conventional are there are multiple competing conventions. The same place absolutely can and will move continents if you decide to swap out one of those conventions for another.

Or consider Cyprus-traditional geography assigns it to Asia-it may be an island, but that’s the nearest continental landmass-and so IANA tzdata lists it as Asia/Nicosia-but since it (or at least the internationally recognised part of it) is in the EU, a lot of people view it as part of Europe. And the standard name for its time zone is “Eastern European Time”