I have 2 Youtube accounts on which I watch completely diffent types of videos. One is on Chrome, the other inside a Firefox Container. When I do a google search or just browse something in Chrome, the YT account inside FF will recommend me videos related to the search / browsing, even if they're not at all related to the videos I watch on that account. The YT account on FF will also regularly suggest me videos related to the ones I watch on my Chrome YT account.
The reverse doesn't happen: my DDG searches and FF browsing never bleed on Youtube.
Google (and many others) doesn't care about private mode, separate accounts, profiles or containers.