Not OP, but I have a dedicated gaming PC connected to a TV for a similar experience (Bazzite for the OS, primarily running Steam Big Picture Mode). Plex HTPC has been pretty smooth to switch between when not gaming. I would recommend using something like VacuumTube (has adblock and sponsorblock settings baked in) to have a more comparable TV experience if you’re looking to watch YouTube too.
Edit: Since you mentioned Jellyfin (haven’t tried using it yet) Switchfin looks to be a Jellyfin HTPC equivalent you could use