Audio Hijack is good, actually
I’d bought pretty heavily into the iTunes ecosystem primarily because it gave me a good listening experience, but also because it had good interoperability with Apple’s AirPlay devices. But ever since upgrading to Catalina, AirPlay has refused to work for completely inscrutable reasons. I’d kind of given up on whole-home music streaming (and was thinking of getting a small FM transmitter and an analog tuner, like I did back in grad school) but then I remembered that I had a generic Bluetooth receiver that I’d bought for use in my previous car.
So, after a little bit of setup and verifying that my desktop could actually communicate to it from across my home, I was going to do the obvious thing and just set up a multi-audio output device to pipe Music.app through.