alt Hacker NewsKodi isn't a media server. Plex isn't FLOSS. Emby is what Jellyfin was forked from, and barely classifies as FLOSS anymore, and isn't as popular as Jellyfin from what I can tell. There isn't really anything else that I am aware of. Jellyfin being the #1 FLOSS media server makes sense to me, although I don't think there are really any viable #2s.
Kodi does have bultin server functionality (both DNLA and a web interface), it's just less commonly used that way, and I don't think transcoding is supported without plugins.