Apple Music Multi-Speaker Playback Fails Between HomePod and Studio Display

Ever since I got my first-gen HomePod, I’ve had this super annoying issue: when I play music, either the audio on my Studio Display doesn’t work (I have to uncheck and recheck it in Apple Music for sound to come out), or the HomePod doesn’t play until I do the same thing with its checkbox.

This problem has been going on for years, and it’s extremely frustrating. Has anyone else experienced this? Has it been officially reported?

[Edited by Moderator]