Having a single, central receiver to collect inputs from 5+ A/V sources and deal them back, arbitrarily? to 6 different outputs seems awfully complicated. Something like Jellyfin or mythtv with one or more TV tuners would let you originate all of the TV & streaming signals from your central source to client players - kodi or whatever - in the player rooms. Most of those have at least some control through homeassistant. Kodi on RPis with some basic class D amplifiers in each room, run through the TV, if the room has a TV. Probably couldn’t get synchronized audio in all rooms that way.
If you get rid of the asshole we elected, you get an asshole we didn’t elect. An asshole we didn’t even have a voice on.