Jellyfin is a fork of Emby due to some drama I can't quite remember. Last I used Emby a few years ago, both looked and operated basically the same as each other.

Jellyfin has made improvements since. I can't speak for Emby since I switched to Jellyfin.

They are not making a Linux build, but they are making sure the Windows build plays nice with Proton. At least that's how I read that.