Linux only but mythbackend has a pretty strong scheduler, srs. I've barely looked at it and don't need to but will detect conflicts in schedules and defer a recording to a later showing if needed, will when 2 or more (depending on a max limit set) happen to fall on the same multiplex just use one tuner, allow preferences for HD versions, specify a particular tuner for a job, etc. I think tvheadend is the other main Linux one.

Mythtv also contains a DLNA/upnp media server but I've largely moved away from that. The cross platform Jellyfin works better for that for me.