Freetube still kind of loses on privacy when using the youtube backend, since invidious is basically dead. Yeah you don't have ads or the youtube client code, but you're still contacting google servers with the content you watch. They have very aggressive rate limits, require session cookies (which can track your watching habits), and aggressive IP-based banning. You can't watch 18+ rated content, which turns out to be more than I thought, comedy most obviously.
There really is no way to get away from it anymore. Most solutions require a clean residential IP, and a cookie of some sort, pooled (from community services) or linked to an account.
Using local downloading tool like pinchflat at least hides your watching patterns from Google, instead of knowing exactly when you watch a video and roughly where in the stream where you started/stopped, they can just see you downloaded a set of videos a 12am every day, regardless of if/when you watch it.