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/components/auth/google-sign-in-button.tsx

@@ -0,0 +1,50 @@
+"use client";
+/**
+ * Google 登录按钮（GIS 渲染）
+ *
+ * 原始 Dart: lib/ui/auth/widgets/google_sign_in_web.dart
+ *
+ * 通过 `google.accounts.id.renderButton` 把 GIS 官方按钮渲染到指定 div。
+ * 登录成功由 `setOnGoogleSignInSuccess` 设置的回调处理。
+ */
+import { useEffect, useRef } from "react";
+
+import {
+  renderGoogleButton,
+  setOnGoogleSignInSuccess,
+  type GoogleSignInSuccess,
+} from "@/integrations/google-identity";
+import styles from "./google-sign-in-button.module.css";
+
+export interface GoogleSignInButtonProps {
+  onSuccess: (success: GoogleSignInSuccess) => void;
+}
+
+export function GoogleSignInButton({ onSuccess }: GoogleSignInButtonProps) {
+  const ref = useRef<HTMLDivElement | null>(null);
+
+  useEffect(() => {
+    setOnGoogleSignInSuccess(onSuccess);
+    return () => setOnGoogleSignInSuccess(null);
+  }, [onSuccess]);
+
+  useEffect(() => {
+    if (!ref.current) return;
+    let cancelled = false;
+    // GIS 异步加载，轮询直到可用
+    const tryRender = () => {
+      if (cancelled) return;
+      if (window.google?.accounts?.id) {
+        renderGoogleButton(ref.current!, { theme: "outline", size: "large" });
+      } else {
+        setTimeout(tryRender, 100);
+      }
+    };
+    tryRender();
+    return () => {
+      cancelled = true;
+    };
+  }, []);
+
+  return <div ref={ref} className={styles.slot} />;
+}