That's a machlokes (I believe) R Elyashiv and R Shlomo Zalmen
Source?
And other drinks as well as food seem to be shaila as to why it's any diff than water, linyan yom kippur, (although have not found a posek who says it's muttar) it's not necessarily the same halacha as every motsie shabbos
Excuse me for not quoting exact sources, I'm not with my books. I'll be happy to if you pm me later.
It may be that r elyashiv is machmir but the mekal is not just rsz auerbach. Iirc it's explicit in shua harav, and almost explicit in mishna berura. (R elyashiv is often more machmir)
The point is that the prohibition to eat on yk finishes as soon as tosefes Yom Kippur does, I.e. A short while after three stars.
At that point a new prohibition starts. Namely, don't eat or drink or do melacha until you have made havdala (over wine for eating and just saying baruch hamavdil for melacha).
This is nothing unique to yk, every shabbos has this. And al pi halacha it does not apply to drinking water as is explicit in gemara and shu"a.
However the mekubalim are strict about drinking water - see sources quoted in kaf hachaim hil. Havdala.
Btw, by the same token, If you're in middle of a meal on the last day of pesach and your meal continues into the night, you are allowed to have chometz in that meal without making any king of havdala, and you can still say yalle veyavo in bentching. And the same would apply to eating out of the Sukah at the end of sukos.