Implement Push Notification Service

Structure PushNotificationService as a Riverpod AsyncNotifier that subscribes to all three FirebaseMessaging streams in its build method. The background message handler must be a top-level async function (not a method) — place it in a dedicated notifications_background_handler.dart file. In main.dart, call FirebaseMessaging.onBackgroundMessage(backgroundMessageHandler) before runApp(). For the foreground in-app banner, use an OverlayEntry inserted into the root overlay; create a custom BannerWidget that auto-dismisses after 4 seconds using a Timer.

For Android foreground notifications, configure flutter_local_notifications with a high-importance channel. Store a StreamController for unreadCount — increment on insert, recompute on mark-all-read. The background handler needs its own Supabase.initialize() call since it runs in a separate isolate — use flutter_secure_storage to retrieve credentials or hardcode the anon key (never service role).

Unit tests: mock FirebaseMessaging streams and assert NotificationRepository.insert() is called with correct payload for each lifecycle path. Test idempotency: calling handler twice with same message_id results in one DB record. Test preference filtering: foreground banner suppressed when category disabled. Test unreadCount stream emits correct value after insert and after mark-as-read.

Integration test: full foreground message flow using fake async and mocked overlay. Widget test: verify badge count updates when unreadCount stream emits. Test background handler function in isolation with mocked Supabase client.