Phase 3 scaffold: chat engine (WebSocket, FCM, pricing, timer, extension, history)

- Backend: WebSocket plugin, chat/pricing/timer/extension/closure/notification services
- Client app: ChatBloc, pricing dialog, chat screen with message status, extension/goodbye flow, history
- Mitra app: MitraChatBloc, ExtensionBloc, chat screen, extension accept/reject, history
- Control center: free trial, extension timeout, early end config toggles
- DB migration: chat_messages, session_closures, session_extensions, customer_transactions tables

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

client_app/pubspec.lock

@@ -57,6 +57,14 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "1.19.1"
+  crypto:
+    dependency: transitive
+    description:
+      name: crypto
+      sha256: c8ea0233063ba03258fbcf2ca4d6dadfefe14f02fab57702265467a19f27fadf
+      url: "https://pub.dev"
+    source: hosted
+    version: "3.0.7"
   dio:
     dependency: "direct main"
     description:
@@ -153,6 +161,30 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "2.17.5"
+  firebase_messaging:
+    dependency: "direct main"
+    description:
+      name: firebase_messaging
+      sha256: a1662cc95d9750a324ad9df349b873360af6f11414902021f130c68ec02267c4
+      url: "https://pub.dev"
+    source: hosted
+    version: "14.9.4"
+  firebase_messaging_platform_interface:
+    dependency: transitive
+    description:
+      name: firebase_messaging_platform_interface
+      sha256: "87c4a922cb6f811cfb7a889bdbb3622702443c52a0271636cbc90d813ceac147"
+      url: "https://pub.dev"
+    source: hosted
+    version: "4.5.37"
+  firebase_messaging_web:
+    dependency: transitive
+    description:
+      name: firebase_messaging_web
+      sha256: "0d34dca01a7b103ed7f20138bffbb28eb0e61a677bf9e78a028a932e2c7322d5"
+      url: "https://pub.dev"
+    source: hosted
+    version: "3.8.7"
   flutter:
     dependency: "direct main"
     description: flutter
@@ -557,6 +589,14 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "0.5.1"
+  web_socket_channel:
+    dependency: "direct main"
+    description:
+      name: web_socket_channel
+      sha256: "58c6666b342a38816b2e7e50ed0f1e261959630becd4c879c4f26bfa14aa5a42"
+      url: "https://pub.dev"
+    source: hosted
+    version: "2.4.5"
   xdg_directories:
     dependency: transitive
     description: