Personally, I have a GUI-less server that is connected to my lan running jellyfin server and an nvidia shield plugged to the TV with an alternative launcher to get rid of ads. That way, the server consumption is low and always on and you get a good interface and a remote for the TV.
If you really want a Linux device plugged to the TV, you could look into Plasma Bigscreen, a KDE made for TV.
Right, it’s still in dev. But could be something to look at, in the future.