Our AIR desktop applications (compiled with AIR 31 SDK - captive runtime bundle) are working great on macOS Big Sur. So you don't have to use the latest Harman AIR 33 SDK on this OS. I believe that the only OS that requires Air 33 at the moment is Android if you want to distribute your application via the Google Playstore.
Regarding update, your are right : when compiling with the the captive runtime bundle option you have to develop your own update system. Vincent. -- Sent from: http://apache-flex-users.2333346.n4.nabble.com/