Hyperpipe (self-hostable YTMusic frontend) supports accounts, which allows for syncing between devices. It really needs an app on at least mobile for it to really be worth it though, as right now it can only be used through the web UI.

I think the claims I’ve heard irl are something along the lines of “can’t trust Google search results, they’re censoring 'em!” I figure the things they’re mad Google “censors” are probably literal or borderline fascist content - and I also tend to assume they’re probably misusing the word censor. I think the tenuous connection here is just that yeah Google is probably doing some shady stuff with their search results.