Does MDM support configuration profiles for managed apps on macOS? In documentation (https://developer.apple.com/documentation/devicemanagement/get_app_configuration) it says 10.15+, but in Command Availability section macOS is not mentioned.
If not, is there any other way to configure macOS app deployed via MDM?
You can simply create a custom configuration profile for any app preference domain and distribute it via MDM. You can either use the app domain directly or the older MCX domain when targeting the Mac with settings.
Currently an app on the Mac will read the settings in its preference domain and apply them. It's up to the app to mark if they came from a managed domain or not. The introduction of the managed app payload makes me think that store apps might need to declare what can be managed in the future, like iOS does now, but that hasn't happened yet.
To be clear, you only want to look at "Command Availability". The Availability details in the sidebar is not relevant in this context since it relates to binary APIs.
Currently Mac should use Managed Preferences instead. When using Managed Preferences (MCX) payloads on Mac, make sure not to include anything sensitive. That payload will install settings to the "/Library/Managed Preferences" folder where it is easy to read them with the defaults command. They also appear in System Preferences.
I wouldn't be surprised if Apple makes these iOS App Settings universal one day. MCX settings are a throwback to Open Directory and might see modernization treatment someday.