feat(frontend): add React SPA with chat, auth, and admin pages

- Vite 6 + React 19 + TypeScript + Tailwind 4 + Zustand 5
- Login page with JWT auth
- Chat interface: MessageList, ChatInput, ChatContainer
- WebSocket hook with auto-reconnect and exponential backoff
- Sidebar with new chat button + session navigation
- Admin dashboard placeholder
- 57 modules, 242KB JS, TypeScript zero errors

frontend/web/src/App.tsx

@@ -0,0 +1,31 @@
+import { Routes, Route, Navigate } from 'react-router-dom'
+import { useAuthStore } from './store/authStore'
+import AppLayout from './components/layout/AppLayout'
+import ChatPage from './pages/chat/ChatPage'
+import DashboardPage from './pages/admin/DashboardPage'
+import LoginPage from './pages/LoginPage'
+
+export default function App() {
+  const isLoggedIn = useAuthStore((s) => s.isLoggedIn)
+
+  if (!isLoggedIn) {
+    return (
+      <Routes>
+        <Route path="/login" element={<LoginPage />} />
+        <Route path="*" element={<Navigate to="/login" replace />} />
+      </Routes>
+    )
+  }
+
+  return (
+    <AppLayout>
+      <Routes>
+        <Route path="/" element={<Navigate to="/chat" replace />} />
+        <Route path="/chat" element={<ChatPage />} />
+        <Route path="/chat/:sessionId" element={<ChatPage />} />
+        <Route path="/admin/dashboard" element={<DashboardPage />} />
+        <Route path="*" element={<Navigate to="/chat" replace />} />
+      </Routes>
+    </AppLayout>
+  )
+}