I have had the same issue after getting permission for Family Control over a month ago for my main app. I have made new Profiles, new certificate, accurate identifiers for both the main app and the DAME (DeviceActivityMonitorExtension). But still only my main app is showing distribution entitlement for family control

I am not completely sure this fix works but it seems like it is working. FC is so complicated by Apple so it is hard to tell. But I do get an app with the DAME extension archived and distributed on App Store without the warnings about permissions. The permission do seem to be given to the extension if you only request them the main app. I only have the FC capability added to my Main app and do not have them in my entitlements or in the capabilities of the extension. I do use ‘import family control’ in my extension as well as the main app and it seems to allow usage in the extension .swift file. Hope this helps someone.