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/components/layout/AppLayout.tsx

@@ -0,0 +1,18 @@
+import { ReactNode } from 'react'
+import { useAuthStore } from '../../store/authStore'
+import Header from './Header'
+import Sidebar from './Sidebar'
+
+export default function AppLayout({ children }: { children: ReactNode }) {
+  const { username, logout } = useAuthStore()
+
+  return (
+    <div className="h-screen flex flex-col bg-gray-950 text-gray-100">
+      <Header username={username} onLogout={logout} />
+      <div className="flex-1 flex overflow-hidden">
+        <Sidebar />
+        <main className="flex-1 overflow-auto">{children}</main>
+      </div>
+    </div>
+  )
+}