Fix auth: auto-create customer, display name flow, OTP auto-verify

- Backend: getOrCreateCustomer with phone fallback for re-login
- Backend: PATCH /api/client/auth/profile for display name update
- Client app: AuthNeedsDisplayNameData state + SetDisplayNameScreen
- Client app: ApiClient.patch method
- Both apps: handle verificationCompleted for auto-verify (test numbers)
- Both apps: skip credential sign-in if already auto-verified
- Remove debug prints from mitra auth + OTP screens
- Fix ChatRequestNotifier.startListening skips when accepting

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

client_app/lib/core/api/api_client.dart

@@ -32,4 +32,9 @@ class ApiClient {
     final response = await _dio.get(path, queryParameters: queryParameters);
     return response.data as Map<String, dynamic>;
   }
+
+  Future<Map<String, dynamic>> patch(String path, {Map<String, dynamic>? data}) async {
+    final response = await _dio.patch(path, data: data);
+    return response.data as Map<String, dynamic>;
+  }
 }