Does the smart tv use the app or are you watching in a browser there? Because with the former they could just use gms to identify you even if you're not logged into the app directly.
This is basically why I strip off googleware and recompile every app I run on grapheneos (and why after 4 weeks of evening debugging I still don't have working protonmail on my phone, ugh)
Yes, I'm sure I'm identified on my smart tv. It's what my family uses for everything. My graphene pixel rarely lets me watch a youtube video. I don't use any Google apps on the graphene, but it sounds like I have more security holes than what you are doing. You're obviously pretty in tune with this stuff. Have you ever compared notes with @final about graphene here? He's actually one of their developers, I believe.
So graphene is the starting point, because it offers security (and sandboxes google play.) F-droid has reasonable policies to protect you from spyware by excluding non-open framework use (I'm not sure if gms is allowed.) This is already 200x better than any app you download from the play store.
However, if you're an actual target because of what you work on and a somewhat-pleb, then applying "don't trust, verify" becomes really important. So I just download source for everything, review the code (search for patterns), remove all the crap like gms, remote debuggers, call-home functions that aren't needed (they never are) and compile it. Then I packet capture the app and use it and see what it does on the network side, and audit storage.
This is way too much work if you're not a target. Just using f-droid should be good enough.
I have been mostly using Obtainium and the zapstore (nostr based). Do you have opinions on those. I was steered away from fdroid a while ago for reasons I don't remember.
gms, remote debuggers, call-home functions that aren't needed (they never are) and compile it. Then I packet capture the app and use it and see what it does on the network side, and audit storage.