I think the first decision to make is pre built vs DIY. The most common pre built solution would be something like Synology. You may start researching there and see if that would fit your needs, or what people do as alternatives.
I personally built one with a similar use case and use Unraid for my OS. The other normal option is TrueNAS.
With that budget you’ll be able to get a good result.
I mainly use torrents but do have Usenet as a backup. I solely have a 4tb block also from NewsGroupDirect. I got it for like 7$ a couple years ago and am still working through it. It’ll last a while. I’ve been pretty satisfied with availability and retention, although YMMV. if I could give advice it’s that a lot of places do really good holiday/black Friday deals.
*arrs / Jellyfin on a custom NAS running unRAID
For my daily driver tv, it’s an android TV with the projektivity launcher (maybe spelled that wrong, but I’m pretty sure there’s a k in there). It is a huge improvement over the stock launcher.
I’m also working on a media TV for my wife that’s actually a NUC running mint. Suboptimal distro choice but I want her to be able to use it as a desktop if she needs. On top of that is flex launcher to launch Jellyfin, YouTube, steam link, etc.
I had tried to make KDE bigscreen work but just could not get installed for the life of me.
A lot of people use The trash guides
The Servarr Wiki is useful as well
I had a similar problem recently on windows. Qbittorrent (version 4.5.3 ish? Don’t quote me) bound to paid proton VPN. Torrents would be added automatically by sonarr, but remain “stalled” until I restarted qbittorrent with administrator permissions. It would work for a day before it stalled out again and I had to manually restart it. Happened for months. Never figured out why.
Are you using the binhex image by any chance? I had this same problem, just had to update it from the apps/community center page instead of from the docker page.