Add a "Send test notification" button to verify push delivery

Adds POST /api/notifications/test, which delivers a canned test push to every
registered device through the existing relay path (not persisted to the
notifications list), wired into the router and OpenAPI. In Settings, a "Send test
notification" button appears under the push toggle, only when push is enabled on
this device, so the full backend -> relay -> FCM -> APNs -> device path can be
verified on demand without waiting for a real device event.

Backend, API and widget tests added; clippy and dart analyze clean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/test/api/notifications_api_test.dart

@@ -36,6 +36,15 @@ void main() {
     await BackendAPI.instance.markAllNotificationsAsRead();
   });
 
+  test('sendTestNotification POSTs to /notifications/test', () async {
+    adapter.onPost(
+      '/notifications/test',
+      (server) => server.reply(200, null),
+    );
+
+    await BackendAPI.instance.sendTestNotification();
+  });
+
   test(
     'listNotifications sends is_new + pagination and reports the total',
     () async {