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/router.dart

@@ -7,6 +7,7 @@ import 'features/auth/screens/display_name_screen.dart';
 import 'features/auth/screens/register_screen.dart';
 import 'features/auth/screens/otp_screen.dart';
 import 'features/auth/screens/force_register_screen.dart';
+import 'features/auth/screens/set_display_name_screen.dart';
 import 'features/splash/splash_screen.dart';
 import 'features/home/home_screen.dart';
 import 'features/chat/screens/searching_screen.dart';
@@ -55,6 +56,7 @@ GoRouter buildRouter(Ref ref) {
       if (data is AuthAuthenticatedData || data is AuthAnonymousData) {
         return (isSplash || isAuthRoute) ? '/home' : null;
       }
+      if (data is AuthNeedsDisplayNameData) return '/auth/set-name';
       if (data is AuthForceRegisterData) return '/auth/force-register';
       if (!isAuthRoute && !isSplash) return '/welcome';
       if (isSplash) return '/welcome';
@@ -66,6 +68,7 @@ GoRouter buildRouter(Ref ref) {
       GoRoute(path: '/auth/display-name', builder: (_, __) => const DisplayNameScreen()),
       GoRoute(path: '/auth/register', builder: (_, __) => const RegisterScreen()),
       GoRoute(path: '/auth/otp', builder: (context, state) => OtpScreen(phone: state.extra as String)),
+      GoRoute(path: '/auth/set-name', builder: (_, __) => const SetDisplayNameScreen()),
       GoRoute(path: '/auth/force-register', builder: (_, __) => const ForceRegisterScreen()),
       GoRoute(path: '/home', builder: (_, __) => const HomeScreen()),
       GoRoute(path: '/chat/searching', builder: (_, __) => const SearchingScreen()),