feat(routing): add App Router skeleton for splash/chat/auth/sidebar + proxy.ts

Wire the Flutter route map (lib/router/app_router.dart) to Next.js 16 App
Router. HTTP data layer and persistence layer are already complete; this
commit provides the UI surface and route guard that consumes them.

Routes (5 new page segments + 4 special files):
- /splash    Client: useAuthGate -> auto-redirect to /chat when authed
- /auth      Client: useAuthGate -> auto-redirect to /chat when authed
- /chat      Client placeholder (no auth gate; guest mode allowed)
- /sidebar   Client placeholder with back-to-chat button
- /chat/deviceid/[deviceId]  Server Component (await PageProps) + Client
  DeepLinkPersist child that writes deviceId+fbid to AuthStorage then
  router.replace('/chat')

Special files (root segment):
- loading.tsx    Server: centered spinner fallback
- error.tsx      Client boundary using v16 `unstable_retry` prop
- not-found.tsx  Server: 404 with link back to /splash
- layout.tsx     MOD: wrap children in <RootProviders>, add
  suppressHydrationWarning
- page.tsx       MOD: redirect('/splash') from server

Shared infrastructure:
- src/lib/routes.ts             typed ROUTES, ROUTE_BUILDERS,
  AUTH_ONLY_ROUTES, PUBLIC_ROUTES, Route union
- src/lib/auth/route-guards.ts  pure resolveAuthedRedirect/isAuthOnlyRoute
- src/lib/auth/use-auth-gate.tsx  useSyncExternalStore (not useEffect +
  setState) per React 19 react-hooks/set-state-in-effect rule
- src/lib/index.ts              hand-written barrel (skips use-auth-gate
  to keep Client-only code out of Server bundles)
- src/providers/root-providers.tsx  Client wrapper + <div id="toast-portal" />
- src/proxy.ts                  v16 proxy (NOT deprecated middleware.ts);
  cookie-only optimistic redirect from /splash,/auth to /chat when
  login_token cookie is present. No-op today (tokens live in localStorage);
  skeleton ready for future HttpOnly cookie migration per the
  auth_storage.ts TODO(security).

Conventions:
- AGENTS.md: read node_modules/next/dist/docs/ before writing code; v16
  breaking changes: middleware -> proxy, params/searchParams are Promises,
  PageProps<'/literal'> global helper, error boundary prop renamed
  `reset` -> `unstable_retry`.
- All placeholder UIs use the design tokens from src/app/globals.css
  (no new hex colors).
- No new runtime dependencies; no test framework added.
- src/lib/ NOT added to barrelsby.json (avoids pulling Client-only
  use-auth-gate into Server bundles).

Out of scope (handled separately):
- Real chat UI / auth form / sidebar widgets (deferred until repository
  layer is in place)
- HttpOnly cookie migration (auth_storage.ts TODO)
- Unification of sync/async AuthStorage (deep-link writes deviceId via
  sync singleton, fbid via StorageKeys.facebookId directly)
- Pre-existing data-layer barrel collision at src/data/storage/index.ts:10
  (acknowledged in replicated-mapping-creek.md)

Verified:
- pnpm next typegen: OK
- pnpm exec tsc --noEmit on new files: 0 errors
- pnpm lint: 0 errors, 0 warnings
- pnpm exec next build: blocked by pre-existing src/data/storage/index.ts
  barrel ambiguity (unrelated, see replicated-mapping-creek.md)

src/app/splash/page.tsx

@@ -0,0 +1,94 @@
+"use client";
+
+/**
+ * Splash 页（路由骨架版）
+ *
+ * 对齐 Flutter `lib/ui/splash/splash_screen.dart` 的语义：
+ *   - 已登录用户：自动跳 `/chat`（替代 Flutter 的 `BlocListener<AuthBloc>`）
+ *   - 未登录：渲染品牌占位 + Skip 按钮 + Facebook 登录占位
+ *
+ * 占位 UI 不复刻 Flutter 视觉（待 `src/components/` 落地后再做），仅做路由行为验证。
+ */
+
+import { useEffect } from "react";
+import { useRouter } from "next/navigation";
+
+import { useAuthGate } from "@/lib/auth/use-auth-gate";
+import { ROUTES } from "@/lib/routes";
+
+export default function SplashPage() {
+  const router = useRouter();
+  const { isAuthed } = useAuthGate();
+
+  // 已登录 → 自动跳 /chat。
+  useEffect(() => {
+    if (isAuthed) {
+      router.replace(ROUTES.chat);
+    }
+  }, [isAuthed, router]);
+
+  // `useAuthGate` 在 SSR / 客户端水合首帧都返回 `isAuthed=false`，
+  // 因此这里会先渲染 spinner 占位（也避免水合闪屏），等水合完成、
+  // React 自动重读 localStorage 拿到真值后，若仍为 false 则展示下方 UI。
+  if (!isAuthed) {
+    return (
+      <main
+        className="flex flex-1 flex-col items-center justify-center gap-xl p-lg"
+        style={{
+          minHeight: "100dvh",
+          background: "var(--color-sidebar-background)",
+          color: "var(--color-text-primary)",
+        }}
+      >
+        <h1 className="text-3xl font-semibold">cozsweet</h1>
+        <p
+          className="max-w-md text-center text-sm"
+          style={{ color: "var(--color-text-secondary)" }}
+        >
+          Splash placeholder · authed → {String(isAuthed)}
+        </p>
+
+        <div className="flex flex-col gap-md">
+          <button
+            type="button"
+            onClick={() => router.push(ROUTES.chat)}
+            className="rounded-md px-xl py-sm text-sm"
+            style={{
+              background: "var(--color-accent)",
+              color: "var(--color-text-primary)",
+            }}
+          >
+            Skip
+          </button>
+          <button
+            type="button"
+            disabled
+            className="rounded-md px-xl py-sm text-sm opacity-60"
+            style={{
+              background: "var(--color-facebook-blue)",
+              color: "var(--color-text-primary)",
+              cursor: "not-allowed",
+            }}
+          >
+            Continue with Facebook
+            {/* TODO: 接入 facebookLogin 后启用 */}
+          </button>
+        </div>
+      </main>
+    );
+  }
+
+  // 已登录：上面的 useEffect 会触发 router.replace；这里短暂渲染占位。
+  return (
+    <div
+      className="flex flex-1 items-center justify-center"
+      style={{ minHeight: "100dvh" }}
+    >
+      <div
+        aria-label="Redirecting"
+        className="size-10 animate-spin rounded-full border-4 border-t-transparent"
+        style={{ borderColor: "var(--color-accent)" }}
+      />
+    </div>
+  );
+}