feat(client/analytics): GA4 funnel instrumentation + unified home CTA

Add Firebase Analytics (GA4) funnel tracking to client_app:
- AnalyticsService typed wrapper (enum-gated, no PII) + analyticsProvider
- FirebaseAnalyticsObserver on GoRouter (screen_name via nameExtractor)
- user_id = customer UUID, user_type property, set on auth resolve/upgrade
- funnel events: curhat_start, curhat_repeat_start, auth_*, onboarding_usp_view,
  payment_view, payment_method_select, payment_started, pairing_matched/no_bestie
- bottom-sheet events: verif_choice_view/select, bestie_choice_view/select,
  extension_offer_view, chat_extension_requested
- payment_started carries app_instance_id + ga_session_id in the
  /payment-requests body for future server-side stitching (backend ignores)
- curhat_mode_pick screen name disambiguates the chat/call mode picker
  (/payment/method-pick) from the payment-channel picker (/payment/method)
- unify both home CTAs to "Aku Mau Curhat"

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

client_app/lib/main.dart

@@ -1,9 +1,11 @@
 import 'dart:async';
 
+import 'package:firebase_analytics/firebase_analytics.dart';
 import 'package:firebase_core/firebase_core.dart';
 import 'package:firebase_messaging/firebase_messaging.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
+import 'core/analytics/analytics_service.dart';
 import 'core/api/api_client_provider.dart';
 import 'core/auth/auth_notifier.dart';
 import 'core/auth/auth_providers_provider.dart';
@@ -28,6 +30,12 @@ void main() async {
 
   await Firebase.initializeApp(options: DefaultFirebaseOptions.currentPlatform);
 
+  // Enable GA4 collection. Fire-and-forget so it never adds to cold-start
+  // latency; the SDK queues events until collection is on.
+  unawaited(
+    FirebaseAnalytics.instance.setAnalyticsCollectionEnabled(true),
+  );
+
   final messaging = FirebaseMessaging.instance;
   await messaging.requestPermission();
 
@@ -131,9 +139,41 @@ class _AppState extends ConsumerState<App> with WidgetsBindingObserver {
     });
   }
 
+  // Tracks the last user_id pushed to GA4 so we don't re-issue identical
+  // setUserId/user-property calls on every transient auth emission.
+  String? _analyticsUserId;
+
+  /// Mirror auth state into GA4 identity (§4): opaque customer UUID as
+  /// `user_id` + `user_type` property. Re-set on identity upgrade
+  /// (anon→verified) so the same user continues. Never sets phone/name.
+  void _syncAnalyticsIdentity(AuthData? data) {
+    final analytics = ref.read(analyticsProvider);
+    final (String? customerId, AnalyticsUserType? userType) = switch (data) {
+      AuthAnonymousData d => (d.customerId, AnalyticsUserType.anonymous),
+      AuthForceRegisterData d => (d.customerId, AnalyticsUserType.anonymous),
+      AuthAuthenticatedData d => (
+          d.profile['id'] as String?,
+          AnalyticsUserType.verified,
+        ),
+      AuthNeedsDisplayNameData d => (
+          d.profile['id'] as String?,
+          AnalyticsUserType.verified,
+        ),
+      _ => (null, null),
+    };
+    if (customerId == _analyticsUserId) return;
+    _analyticsUserId = customerId;
+    // ignore: discarded_futures
+    analytics.setUserId(customerId);
+    if (userType != null) {
+      // ignore: discarded_futures
+      analytics.setUserType(userType);
+    }
+  }
+
   @override
   Widget build(BuildContext context) {
-    // FCM registration on auth.
+    // FCM registration + analytics identity on auth.
     ref.listen(authProvider, (prev, next) {
       final data = next.valueOrNull;
       if (data is AuthAuthenticatedData || data is AuthAnonymousData) {
@@ -142,6 +182,7 @@ class _AppState extends ConsumerState<App> with WidgetsBindingObserver {
         // Logged out (or initial) — ensure the chat WS is closed.
         ref.read(chatProvider.notifier).disconnect();
       }
+      _syncAnalyticsIdentity(data);
     });
 
     // Global chat WebSocket lifecycle: connect whenever the user has an