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/error.tsx

@@ -0,0 +1,66 @@
+"use client";
+
+/**
+ * 根级错误边界
+ *
+ * Next.js 16 约定：必须为 Client Component；reset prop 在 v16 中被重命名为
+ * `unstable_retry`（参见 `node_modules/next/dist/docs/01-app/03-api-reference/03-file-conventions/error.md`）。
+ *
+ * 行为：把 `error` 打到 console（保留 digest 便于服务端聚合），并提供"重试"
+ * 与"返回首页"两个动作。
+ */
+
+import { useEffect } from "react";
+import Link from "next/link";
+
+import { ROUTES } from "@/lib/routes";
+
+interface ErrorProps {
+  error: Error & { digest?: string };
+  unstable_retry: () => void;
+}
+
+export default function GlobalError({ error, unstable_retry }: ErrorProps) {
+  useEffect(() => {
+    // 把错误送到 console；后续接 Sentry/Datadog 时改这里。
+    console.error("[app/error.tsx]", error);
+  }, [error]);
+
+  return (
+    <div className="flex flex-1 flex-col items-center justify-center gap-md p-lg">
+      <h1
+        className="text-2xl font-semibold"
+        style={{ color: "var(--color-text-primary)" }}
+      >
+        Something went wrong
+      </h1>
+      <p
+        className="max-w-md text-center text-sm"
+        style={{ color: "var(--color-text-secondary)" }}
+      >
+        {error.message || "Unexpected error"}
+        {error.digest ? ` (digest: ${error.digest})` : null}
+      </p>
+      <div className="flex gap-sm">
+        <button
+          type="button"
+          onClick={unstable_retry}
+          className="rounded-md px-lg py-sm text-sm"
+          style={{
+            background: "var(--color-accent)",
+            color: "var(--color-text-primary)",
+          }}
+        >
+          Retry
+        </button>
+        <Link
+          href={ROUTES.splash}
+          className="rounded-md border px-lg py-sm text-sm"
+          style={{ borderColor: "var(--color-border)" }}
+        >
+          Back to start
+        </Link>
+      </div>
+    </div>
+  );
+}