feat: implement email change request functionality with verification dialog

lib/features/profile/data/profile_repository.dart

@@ -207,6 +207,28 @@ class ProfileRepository {
     }
   }
 
+  /// Request email change: POST /auth/change-email
+  /// Backend sends a verification link to [newEmail]; email is only
+  /// persisted once the link is clicked.
+  Future<String> requestEmailChange(String newEmail, String password) async {
+    try {
+      final response = await _dio.post('/auth/change-email', data: {
+        'newEmail': newEmail,
+        'password': password,
+      });
+      return (response.data?['data']?['message'] as String?) ??
+          'Verification link sent';
+    } on DioException catch (e) {
+      if (e.error is ApiException) throw e.error as ApiException;
+      throw ApiException(
+        message: e.response?.data?['message'] ??
+            e.message ??
+            'Failed to request email change',
+        statusCode: e.response?.statusCode,
+      );
+    }
+  }
+
   /// Fetch notification preferences.
   /// Agent: GET /agents/preferences/notifications
   /// User: GET /users/preferences/notifications