Honestly, you may be overthinking this. For a media server you want something with a fairly recent Intel processor, say a 6th gen or newer i5, i7 or i9, with at least 8 GB of RAM (More is better), and as much storage as you can reasonably afford. The only reason I say go with an Intel CPU is because QuickSync can make transcoding go quicker. The particular model of the PC doesn’t really matter. Anything with these specs will run Home Assistant quite easily as well as most other things you might want.
If you haven’t run across https://perfectmediaserver.com/ you may wish to check it out.
It looks interesting, but I don’t see how it is better than NextCloud, at least in my use case.