I actually have a Mini-PC with an N100 CPU and no dedicated GPU as media server and it uses very little CPU (less than 20%) whilst playing 1080p video even with a torrent server over a wireguard VPN running on the background.

You don't really need much CPU or GPU for playing or streaming videos from compress video files as long as you have hardware decoding on either processing unit (just make sure it implements all the way up to the AV1 coded).

You only need lots of CPU or GPU power if the codec you're decoding from or encoding to is not implemented in hardware since in that case it will use software decoding or encoding so it's down to raw CPU or GPU power.

In fact if all you want is a media server that solution I have is probably one of the best ones, mainly because it uses very little power (tops at 25W, usually much less) and runs silent, which is why I can have it in my living room using it as a media player connected to my TV, and with a wireless remote people can't really tell it's a PC since it just looks and works like a store bought media player rather than one I put together myself.

However that option means buying new stuff, and I can see the value in using old hardware if you have it around, plus the old hardware will still likely be more powerful so you can also use it for more demanding stuff or just more stuff at the same time, which is why I didn't suggest it and instead just suggested some tweaks to make that old hardware consume less and make less noise.