I've opened up a support issue with Apple on this, and it's currently at engineering.
I've noticed that there are several issues - not just one, and much of this has not changed since migrating to 10.15.6
The problem seems to be exacerbated by using a mixture of Airplay and Airplay 2 devices on the network.
However, I'm not sure if this is the case.
The Error message "Could not connect to ”[Device Name]“ " cause Music playback to stop and stall across the network, which is really annoying. One can reset the music by playing a different playlist and then switching back. This doesn't solve the connection problem, just the playback problem.
The above error message is normally paired with another message: "The AirPlay device ”[Device Name]“ cannot be found on your network. Please verify your network settings and AirPlay configuration or select another device." This message times out after about 20 seconds, but it's very misleading (In most cases the network is absolutely fine (one can check with a phone or vendor app to see that the device is connecting fine on the network - and some of them have web pages which one can connect to).
When we see the error "There are no speakers connected to the AirPlay device “[Device Name]”, this actually means that the device is now working and we can playback through it.
Once all the above has taken place, your Remote App will not work any more until you have switched playlists and closed the relevant alerts - which sort of defeats the point of using a remote app.
Resetting the computer, or doing a dns flush does not help the issue. Likewise, making sure that you only have one network port (ie, not wifi AND wired) does not seem to make a difference.
The current workaround we are using - not always reliable - is to keep all the airplay devices on (once you have them all connected and playing) and then leave them all at zero volume rather than switching them on/off. In order for this to work, it's important to turn off power/network standby - and this workaround still is a major pita.