I'm in a similar position to you, tk4679 -- this just started happening to me today. I work in the streaming TV business, so I have some insight into what I think is happening -- and I have a question about how the "Family Plan" impacts this.
In my use case I am definitely playing music on multiple devices at once. I leave music playing at home to keep my pet company on my Sonos, and I also use Apple Music on my iPhone and at work. Like tk4679, I never had an issue doing this until yesterday. I use iCloud Library and iTunes Match and download most of my music to the phone (New York subway and all).
My guess is that Apple's latest update "fixed" or secured their concurrent stream limit technology(which from a commercial perspective they really ought to have always been doing). I notice that my Apple Music shuts off, when it does, when a song changes on one of the two devices, meaning the "heartbeat" technology that sees if a user is still there seems to be tied to a by-the-song basis. My Spotify account has always done this, and I wondered why Apple just didn't seem to bother.
In any event I have a simple question: If I use a Family Plan, does that mean I can also use more than one stream on my same Apple ID? Or put more simply--can I go back to playing Apple Music with my Sonos (logged in via my Apple ID) and my iPhone (logged in via the same Apple ID) as I did before? Streaming TV services all (to my knowledge) work this way, but I want to be sure Apple does the same.