As I just wrote in a post under the previous poster's one, you can use a Mini-PC with a low-power processor like the N100 and a wireless remote and it will definitelly not look or sound like a "big loud box" (not least because the fan almost never goes on and when it goes it's quiet - it turns out that even an N100 is overpowered for just working as a TV box so CPU usage is almost always below 10%).

Further, you can put Linux in it and then manage it remotelly via SSH, so after setting it up you don't need a keyboard or mouse connected to it.

The end result is something that doesn't at all look like a PC and which, thanks to the remote, you use just like a dedicated TV box.

Hardward for reference: Mini-PC, Remote

PS: That PC is a lot more expensive now than when I bought it 2 years ago.

Loud?

You can get a minipc with no fan for a couple hundred bucks.

You control it with a wireless mouse and wireless keyboard.

Or with kde connect using your phone.

Or however you want to control it because it's linux and you can do whatever the fuck you want and use ubkock or pihole or whatever and never see another ad for the rest of your life.

Big loud box describes modern consoles and cable boxes so it's not that big of a deal.

I don’t want a big loud box near a tv.

With mATX or ITX you can make a shockingly small and attractive computer; examples include this mATX case or this ITX case. People have even designed 3d printable cases, plans for laser cut/CNC acrylic and metal, etc.. If that's not small or classy enough, the miniPC market has really taken off and depending on how modest your needs are, you can get by with things like Zimaboards or go all the way to something like the MINISFORUM AI X1 Pro - a very capable machine that has an Oculink port that allows you to connect an external GPU if you need even more power.

Generally speaking you're never driving a media PC hard enough for the fans to ramp up, but if you somehow are, just buy quality fans and/or watercooling. I can speak for Noctua fans not just being a meme; they are actually very quiet.

How would you even control it ?

I have a small keyboard with a built in trackpad. It's a bit bigger than a TV remote but not obnoxiously so, but given you get the ability to actually write stuff in instead of using an onscreen keyboard with an IR remote it's a worthwhile trade.