test(notifications): add positive coverage for new-user install notification

Locks in that register()/setup_admin() actually produce the
"Install AFT as an app" notification, not just that unrelated
count assertions don't regress.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

Author: sjefferson99

server/tests/test_api_notifications.py

@@ -1277,6 +1277,29 @@ def test_delete_all_only_affects_own_notifications(
         )
 
 
+@pytest.mark.api
+class TestMobileAppInstallNotification:
+    """Regression test for Issue 514: new users get a mobile app install notification."""
+
+    def test_new_user_receives_mobile_app_install_notification(
+        self, api_client, second_user_session
+    ):
+        """A freshly registered user should have the 'Install AFT as an app' notification."""
+        response = second_user_session.get(f'{api_client}/api/notifications')
+        assert response.status_code == 200
+
+        notifications = response.json()['notifications']
+        install_notif = next(
+            (n for n in notifications if n['subject'] == 'Install AFT as an app'), None
+        )
+        assert install_notif is not None, (
+            f"Expected an 'Install AFT as an app' notification for a new user, "
+            f"but found subjects: {[n.get('subject') for n in notifications]}"
+        )
+        assert install_notif['unread'] is True
+        assert install_notif['action_url'] == '/settings.html'
+
+
 @pytest.mark.api
 class TestNotificationMultiUserCreation:
     """Test cases for admin creating notifications for all users."""