The suggested solution is to provide no default value to the property and set its value in the initializer instead.

See in the Xcode release notes under Swift 5.6 -> Resolved Issues.

For your code the fix is like this:

@main
struct Pro_Music_2App: App {
    @StateObject var audioPlaybackManager: AudioPlaybackManager
    
    @StateObject var dataController = DataController()

    init() {
        self._audioPlaybackManager = StateObject(wrappedValue: AudioPlaybackManager())
    }    

    var body: some Scene {
        WindowGroup {
            ContentView()
                .environmentObject(audioPlaybackManager.manager)
                .environmentObject(audioPlaybackManager)
                .environmentObject(audioPlaybackManager.manager.playlistManager)
                .environmentObject(audioPlaybackManager.musicPlayerViewManager)
                .environmentObject(audioPlaybackManager.scrubberViewModel)
                .environment(\.managedObjectContext, dataController.container.viewContext)
                
        }
    }
}

@MainActor class AudioPlaybackManager: ObservableObject {
    ...
}

The underlying problem is that initializers are not async. Therefore, you cannot hop between different actors. And since the compiler synthesizes an initializer for default-values, this also affects default-values. That is, if e.g. your DataController was annotated with a different global actor than @MainActor, then the initializer had to hop between the @MainActor and whatever actor you're using on DataController. That, however, is impossible because init cannot be async.

I guess it would be difficult to implement this single-actor check for stored properties' default-values in the compiler, therefore they just decided to not allow actor protected default-values in this context. As a result, we have to write the initializer ourselves.

For reference see: https://github.com/apple/swift-evolution/blob/main/proposals/0327-actor-initializers.md#stored-property-isolation

I had the same issue and I have fixed it in this way:

@MainActor
class MultipleDownloadsViewModel: NSObject, ObservableObject {
    @Published var downloads: [DownloadModel]

    // Init of properties in actor: see https://stackoverflow.com/questions/71396296/how-do-i-fix-expression-requiring-global-actor-mainactor-cannot-appear-in-def/71412877#71412877
    @MainActor override init() {
        downloads = [
            DownloadModel(fileToDownload: "https://speed.hetzner.de/100MB.bin"),
            DownloadModel(fileToDownload: "https://speed.hetzner.de/1GB.bin"),
            DownloadModel(fileToDownload: "https://speed.hetzner.de/10GB.bin")
        ]
    }

    ...
}