Can the NSPersistentCloudKitContainer mirror the data from the cloudKit public database to the local Core Data if the user is not logged in?

That's worth a feedback report with the full logs. NSPersistentCloudKitContainer is supposed to be compatible with account-less public database use.

That's worth a feedback report with a sysdiagnose or the logs from your test run.

Here is the code that works only if the user is logged in. Again, I'm connecting to the Public database.

    class CoreDataManager: ObservableObject{
        // Singleton
        static let instance = CoreDataManager()
        private let queue = DispatchQueue(label: "CoreDataManagerQueue")
        
        private var iCloudSync = true
        
        lazy var context: NSManagedObjectContext = {
        return container.viewContext
        }()
        
        lazy var container: NSPersistentContainer = {
        return setupContainer()
        }()
            
        func updateCloudKitContainer() {
            queue.sync {
                container = setupContainer()
            }
        }
        
        func setupContainer()->NSPersistentContainer{
            let container = NSPersistentCloudKitContainer(name: "CoreDataContainer")
            
            guard let description = container.persistentStoreDescriptions.first else{
                fatalError("###\(#function): Failed to retrieve a persistent store description.")
            }
            
            description.setOption(true as NSNumber, forKey: NSPersistentHistoryTrackingKey)
        
            let cloudKitContainerIdentifier = "iCloud.com.example.PublicDatabaseTest"
                
            let options = NSPersistentCloudKitContainerOptions(containerIdentifier: cloudKitContainerIdentifier)
            description.cloudKitContainerOptions = options
                
            description.cloudKitContainerOptions?.databaseScope = .public // Specify Public Database
            
            container.loadPersistentStores { (description, error) in
                if let error = error{
                    print("Error loading Core Data. \(error)")
                }
            }
            container.viewContext.automaticallyMergesChangesFromParent = true
            container.viewContext.mergePolicy = NSMergeByPropertyObjectTrumpMergePolicy

            return container
        }
        
        func save(){
            do{
                try context.save()
            }catch let error{
                print("Error saving Core Data. \(error.localizedDescription)")
            }
        }
    }

Just to clarify, the error shown in my original post is not an error that makes the app crash, it's an error I get in the debug console, I assume it's an error logged by CloudKit.