> doing something even slightly related to the previous session brings back its entire recommendation history.

Are you sure that it does, and that it's not just a case of "hey we've never seen this person before, but they watched X, let's immediately start with recommendations Y and Z because other people who watched X were engaged with it?"

I used to think that and gave them the benefit of the doubt, but then I realised that some of the videos being recommended had nothing to do with the one currently watched other than the fact I watched similar ones previously.

Yeah, the fact that I can clear cookies, open a private browsing window with tracking protection turned on, go to YouTube, and be asked which of my two gmail accounts I want to log in with, is pretty creepy.

Yes you are right they are using browser fingerprinting, but with the right tool they can easily change it. They can use Kameleo software or Multilogin etc. https://kameleo.io/

How does that work at, say, the library, or some other public internet kiosk? Or maybe they're just assuming these are edge cases today, amidst the billions of private browser instances on handhelds?

It probably doesn’t work, considering the library users would be watching totally different & unrelated videos, where as in my case they have years of data of very specific viewing habits centred around a few topics.