YouTube premium has no ads on the AppleTV app, which solves the TV side for my home. I have to imagine Android TV and other solutions are the same for the most part - is your TV using some kind of odd built in YouTube app that doesn't support the Premium subscription?
The tech in my home also practices diversity and there's Android TV as well as Apple TV - my experience has been the same as yours that Youtube Premium is ad free on all of them.
I have heard some folks using tools like invidious but I'm not sure how well they map to multiple screens.
Being able to put the same account onto the built in youtube apps on TV's and mobile devices has been useful. No need to buy a white noise machine for kids, we just use a google mini in speaker mode only. Sure, I'd like it to be something else but premium has me on board for now.
