Like the others, I suggest you stick to a distro designed for desktop use (Ubuntu, Fedora etc), you’ll have a much easier time.
If you really want to go with something closer to “scratch made” I’d recommend Arch. Its documentation is killer and you can build a system suited to your requirements.
You should try out KDE in a Live CD. The snapping and tiling features work very well, Windows needs to catch up
My method to get around this is setting up a specific user account for my TV. In the user options you can disable transcoding
It is paid for, with your time ;)
Jellyfin? It’s always supported 4K afaik
I use Arch because it makes installing almost any software package trivially easy via the AUR and if you run into issues, the wiki is there to help.