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>

mitra_app/lib/core/auth/auth_notifier.dart

@@ -54,7 +54,11 @@ class MitraAuth extends _$MitraAuth {
       final completer = Completer<void>();
       await _auth.verifyPhoneNumber(
         phoneNumber: phone,
-        verificationCompleted: (_) {
+        verificationCompleted: (credential) async {
+          try {
+            await _auth.signInWithCredential(credential);
+            state = AsyncData(await _verifyAndReturn());
+          } catch (_) {}
           if (!completer.isCompleted) completer.complete();
         },
         verificationFailed: (e) {
@@ -78,7 +82,8 @@ class MitraAuth extends _$MitraAuth {
     try {
       if (kIsWeb && _webConfirmationResult != null) {
         await _webConfirmationResult!.confirm(smsCode);
-      } else {
+      } else if (_auth.currentUser == null) {
+        // Only sign in if not already signed in via auto-verification
         final credential = PhoneAuthProvider.credential(
           verificationId: verificationId,
           smsCode: smsCode,