feat(web): add multiplayer layout route and landing page

- multiplayer.tsx: layout route wrapping all multiplayer children
  with WsProvider, auth guard via beforeLoad
- multiplayer/index.tsx: create/join landing page
  - POST /api/v1/lobbies to create, navigates to lobby waiting room
  - POST /api/v1/lobbies/:code/join to join, normalizes code to
    uppercase before sending
  - loading states per action, error display, Enter key on join input
  - imports Lobby type from @lila/shared (single source of truth)

apps/web/src/routes/multiplayer.tsx

@@ -0,0 +1,21 @@
+import { createFileRoute, Outlet, redirect } from "@tanstack/react-router";
+import { WsProvider } from "../lib/ws-provider.js";
+import { authClient } from "../lib/auth-client.js";
+
+export const Route = createFileRoute("/multiplayer")({
+  component: MultiplayerLayout,
+  beforeLoad: async () => {
+    const { data: session } = await authClient.getSession();
+    if (!session) {
+      throw redirect({ to: "/login" });
+    }
+  },
+});
+
+function MultiplayerLayout() {
+  return (
+    <WsProvider>
+      <Outlet />
+    </WsProvider>
+  );
+}