How to connect Swift actor to a managed object context defined in MainActor isolated stack

I have the following CoreData stack:

@MainActor
final class CoreDataStack {
    static let shared = CoreDataStack()
    let privateContext: NSManagedObjectContext //used for database read/writes, background queue
    let mainContext: NSManagedObjectContext //parent is set to privateContext, operates on main queue, used for UI
    .....
}

I am omitting initialisation as it is not relevant here.

Now I want to define a CloudActor whose job would be to sync data with the cloud service. The most obvious choice would be to restrict this actor to the privateContext, but I struggle to figure out how to achieve this:

final class NSModelObjectContextExecutor: @unchecked Sendable, SerialExecutor {
    final let context: NSManagedObjectContext
    init(context: NSManagedObjectContext) {
        self.context = context
    }
    
    @available(macOS 10.15, iOS 13.0, watchOS 6.0, tvOS 13.0, *)
    func enqueue(_ job: UnownedJob) {
        let unownedExecutor = asUnownedSerialExecutor()
        context.perform {
            job.runSynchronously(on: unownedExecutor)
        }
    }

    public func asUnownedSerialExecutor() -> UnownedSerialExecutor {
        UnownedSerialExecutor(ordinary: self)
    }
}

final actor CloudDelegate {
    static let shared = CloudDelegate()
    private let context:NSManagedObjectContext

    init() {
        // this doesn't work because CoreDataStack is isolated to MainActor
        context == CoreDataStack.shared.privateContext
    }
}

I am using strict concurrency, so I struggle to understand how I can achieve this. I thought about moving initialisation of privateContext to the CloudDelegate, but it just pushes the problem to CoreDataStack where I would lose the ability to call mainContext.parent = privateContext.

At the same time I realise that what I am trying to achieve seems completely reasonable, so there must be a way to do so. I am probably just missing something.

At the moment the workaround I have is to initialise a fresh background context in CloudDelegate which connects directly to the persistent coordinator, but this is obviously less efficient and introduces weird complications with merging (see this)