feat(sync): add background task system for nightly CloudKit sync

Add BGTaskScheduler-based background sync for keeping local data fresh:

- BackgroundSyncManager: New singleton managing background tasks
  - BGAppRefreshTask for periodic CloudKit sync (system-determined frequency)
  - BGProcessingTask for overnight sync + database cleanup (2 AM)
  - Auto-archives games older than 1 year during cleanup

- Info.plist: Added BGTaskSchedulerPermittedIdentifiers
  - com.sportstime.app.refresh (periodic sync)
  - com.sportstime.app.db-cleanup (overnight processing)

- SportsTimeApp: Integrated background task lifecycle
  - Register tasks in init() (required before app finishes launching)
  - Schedule tasks after bootstrap and when app enters background

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

SportsTime/SportsTimeApp.swift

@@ -7,6 +7,7 @@
 
 import SwiftUI
 import SwiftData
+import BackgroundTasks
 
 @main
 struct SportsTimeApp: App {
@@ -14,6 +15,10 @@ struct SportsTimeApp: App {
     private var transactionListener: Task<Void, Never>?
 
     init() {
+        // Register background tasks BEFORE app finishes launching
+        // This must happen synchronously in init or applicationDidFinishLaunching
+        BackgroundSyncManager.shared.registerTasks()
+
         // Start listening for transactions immediately
         transactionListener = StoreManager.shared.listenForTransactions()
     }
@@ -105,11 +110,19 @@ struct BootstrappedContentView: View {
             await performBootstrap()
         }
         .onChange(of: scenePhase) { _, newPhase in
-            // Sync when app comes to foreground (but not on initial launch)
-            if newPhase == .active && hasCompletedInitialSync {
-                Task {
-                    await performBackgroundSync(context: modelContainer.mainContext)
+            switch newPhase {
+            case .active:
+                // Sync when app comes to foreground (but not on initial launch)
+                if hasCompletedInitialSync {
+                    Task {
+                        await performBackgroundSync(context: modelContainer.mainContext)
+                    }
                 }
+            case .background:
+                // Schedule background tasks when app goes to background
+                BackgroundSyncManager.shared.scheduleAllTasks()
+            default:
+                break
             }
         }
     }
@@ -129,17 +142,23 @@ struct BootstrappedContentView: View {
             // 2. Configure DataProvider with SwiftData context
             AppDataProvider.shared.configure(with: context)
 
-            // 3. Load data from SwiftData into memory
+            // 3. Configure BackgroundSyncManager with model container
+            BackgroundSyncManager.shared.configure(with: modelContainer)
+
+            // 4. Load data from SwiftData into memory
             await AppDataProvider.shared.loadInitialData()
 
-            // 4. Load store products and entitlements
+            // 5. Load store products and entitlements
             await StoreManager.shared.loadProducts()
             await StoreManager.shared.updateEntitlements()
 
-            // 5. App is now usable
+            // 6. App is now usable
             isBootstrapping = false
 
-            // 6. Background: Try to refresh from CloudKit (non-blocking)
+            // 7. Schedule background tasks for future syncs
+            BackgroundSyncManager.shared.scheduleAllTasks()
+
+            // 8. Background: Try to refresh from CloudKit (non-blocking)
             Task.detached(priority: .background) {
                 await self.performBackgroundSync(context: context)
                 await MainActor.run {