Apple Music Home Sharing: Skips song and doesn't play audio when Bluetooth speakers/headphones are connected

Since a while back, I can't get Apple Music's Home Sharing (Media Sharing) to work on the local network. If I access the library on another MacOS computer, the library content will display fine, but nothing can be played if I'm using Bluetooth speakers/headphones (AirPods Pro, or AirPods Max in my case). Whenever I attempt to play a track, it will skip the track in question and instead jump to the next track. It will then look as if that track is playing (red sound wave animation), but it is stuck at 00:00 and no audio is played. This problem does not occur when playing through the on-board speakers. Playback then is fine. The problem occurs only when the "Airplay" icon (top right corner with concentric rings and a small triangle) is red, which happens when Bluetooth speakers are connected. If Bluetooth is off or no Bluetooth speakers are connected, that icon will be gray. I am not sure when this occurred, perhaps when I moved my Mac to another Mac via Time Machine restoration. This issue has been persistent over MacOS 12 and MacOS 13. What I have tried: * Reset Media Sharing in System Settings * Reset MacOS Firewall in System Settings * Reset Handoff and "Allow AirPlay" in System Settings * Unpairing, factory resetting, re-pairing Bluetooth headphones * Reset "Music Store cache" in Apple Music * Reset "Music Media folder location" in Apple Music I am wondering if someone else has experienced this problem, and if you found a solution. Or if not, at least that may indicate that this is a wider problem that people are having. It might be a bug in MacOS/Apple Music. I don't know how to contact Apple about this issue. --- NB: Additionally, it seems like the Mac trying to access the remote library, is unable to AirPlay to the Mac that has the remote library. However, the reverse works. Settings on both Macs allow Handoff and to act as an "AirPlay receiver" for "Current User" (I am logged in on the same Apple ID on both Macs).