Well your guess is correct. I had the same issue, no airplay in the normal sound controls, only in the Music app. After installing my Fenvi t919 wifi/bluetooth adapter card I now have Airplay option in the sound control as it was before in Catalina and so on.
Note: Initially I had no wifi card whatsoever and a cheap bluetooth usb dongle. Removed the dongle and installed the Fenvi pci card and now Airplay is working system wide and also Airdrop and Handoff. (Bluetooth still needs an usb connection, cable provided by Fenvi in my case)
Hopefully you'll get it sorted as well...