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/not-found.tsx

@@ -0,0 +1,39 @@
+/**
+ * 根级 404
+ *
+ * Server Component。覆盖未匹配路由（结合 `notFound()` 调用）。
+ * 不启用 v16 实验性 `global-not-found.js`，避免 `next.config.ts` 变更。
+ */
+
+import Link from "next/link";
+
+import { ROUTES } from "@/lib/routes";
+
+export default function NotFound() {
+  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)" }}
+      >
+        Page not found
+      </h1>
+      <p
+        className="max-w-md text-center text-sm"
+        style={{ color: "var(--color-text-secondary)" }}
+      >
+        The page you&apos;re looking for doesn&apos;t exist or has been moved.
+      </p>
+      <Link
+        href={ROUTES.splash}
+        className="rounded-md px-lg py-sm text-sm"
+        style={{
+          background: "var(--color-accent)",
+          color: "var(--color-text-primary)",
+        }}
+      >
+        Return to start
+      </Link>
+    </div>
+  );
+}