Issues connecting AirPods Max and other headphones to MacBook

Question

When AirPods Max is connected to macOS (11.2.2) my Bose QC 35 II headset can not hold a connection any more. I can try to connect to the Bose but it will immediately lose the connection. When I drop the connection from macOS to the AirPods Max, the Bose will happily connect.

Does anyone know how to solve this problem and keep both connected at the same time?

I deleted the Bluetooth plist and restarted macOS (which solved another Bluetooth device problem), but it didn't help this issue.