feat(ui): migrate Flutter UI library to Next.js 16 (App Router)

Migrate all 87 Dart files from /Users/chase/Documents/cozsweet/lib/ui/
to TypeScript React components, replacing Flutter-native features with
Web equivalents and reimplementing the BLoC pattern with React
Context + useReducer.

Highlights
- 1:1 BLoC -> Context+useReducer+side-effects mapping for auth, chat,
  user, and sidebar features (4 providers wired in root-providers.tsx)
- 500px MobileShell primitive eliminates per-screen layout boilerplate
- Headless Dialog primitive (createPortal + ESC + scroll lock) powers
  quota / pwa-install / username / pronouns / subscription / other-options
  dialogs
- New integrations/: facebook-sdk, google-identity, pwa-install,
  media-recorder (Web Speech API + MediaRecorder), browser-detect,
  chat-websocket (singleton), message-queue (throttled send)
- CSS Modules + existing design tokens (no new styling system);
  extended with breakpoints.css and dimensions.css
- Custom hooks: useBreakpoint (useSyncExternalStore),
  useFullVisibility (IntersectionObserver), usePwaInstall,
  usePullToRefresh
- Vitest + jsdom; 15 unit tests (chat-reducer, auth-validators)
- React 19.2.4, Next.js 16.2.7, Zod 4, lottie-react, classnames

Workarounds
- next.config.ts: experimental.staticGenerationRetryCount = 0 to
  bypass Next.js 16.2.7 /_global-error workStore prerender bug
- src/app/global-error.tsx: required Client Component
- src/types/globals.d.ts: centralized window.google / FB /
  SpeechRecognition declarations

Routes (/, /splash, /auth, /chat, /chat/deviceid/[deviceId],
/sidebar) all build and lint clean.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

src/app/chat/page.tsx

@@ -1,53 +1,7 @@
 "use client";
 
-/**
- * Chat 页（路由骨架版）
- *
- * **不**做鉴权重定向：Flutter 端允许游客态直接进聊天（`auth_refresh_interceptor`
- * 会同时处理登录与游客 token）。这里只放占位 UI。
- */
-
-import Link from "next/link";
-
-import { ROUTES } from "@/lib/routes";
+import { ChatScreen } from "@/components/chat/chat-screen";
 
 export default function ChatPage() {
-  return (
-    <main
-      className="flex flex-1 flex-col items-center justify-center gap-xl p-lg"
-      style={{
-        minHeight: "100dvh",
-        background: "var(--color-page-background)",
-        color: "var(--color-text-foreground)",
-      }}
-    >
-      <h1 className="text-3xl font-semibold">Chat</h1>
-      <p
-        className="max-w-md text-center text-sm"
-        style={{ color: "var(--color-text-secondary)" }}
-      >
-        Chat placeholder · guest mode supported · real chat UI coming soon.
-      </p>
-
-      <div className="flex flex-col gap-md">
-        <Link
-          href={ROUTES.sidebar}
-          className="rounded-md border px-xl py-sm text-center text-sm"
-          style={{ borderColor: "var(--color-border)" }}
-        >
-          Open Sidebar
-        </Link>
-        <Link
-          href={ROUTES.auth}
-          className="rounded-md px-xl py-sm text-center text-sm"
-          style={{
-            background: "var(--color-accent)",
-            color: "var(--color-text-primary)",
-          }}
-        >
-          Log in
-        </Link>
-      </div>
-    </main>
-  );
+  return <ChatScreen />;
 }