I'm also interested in this. I've seen that used mini PCs can be found for under $100, which is still pretty pricey for this need imo, but I'm sure it's a good choice for setting up a Jellyfin server and maybe some general home management type stuff like security cameras or smart lights or something. If you already have a PC, you might be better off using that to grab media and then throw it onto a drive that you can connect to the USB of your TV if it has one. Alternatively, maybe run a long HDMI from PC to TV? Or maybe something like a Steam Link could get that done? Combine that with a phone app to control your PC from another room and you're in business. It really depends on the volume you're looking to watch though because that would be a headache to do more than just a few times per week. I wish I could be more helpful to you, but I'm just some spitballing idiot who also doesn't know until somebody with more experience chimes in lol.

I myself am flirting with the idea of building a gaming desktop that could fill this role as well as serve as a modern Steam Machine running Chimera OS. I bought a used Steam Deck a while back and fell in love with the UX, but while it's amazing for a handheld it's a little underpowered for gaming at home. I have built a few Windows PCs about ten years ago, but any nuggets of wisdom regarding differences today, Linux tips, etc would be greatly appreciated. I've done a bit of homework, but people on Lemmy seem to be super knowledgeable about this kind of thing.