ci: make the logout pending-state test deterministic (gate, not delay)

Same timing-window race as object-new-page: the 50ms delay let the logout
resolve (menu unmounts on me=null) before findByText caught 'Signing out…'
on the slow CI runner. Hold the logout open with a promise released only
after the pending state is asserted.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

web/src/shell/user-menu.test.tsx

@@ -1,7 +1,7 @@
 import { expect, test } from "vitest";
 import { screen, waitFor, within } from "@testing-library/react";
 import userEvent from "@testing-library/user-event";
-import { delay, http, HttpResponse } from "msw";
+import { http, HttpResponse } from "msw";
 import { server } from "../test/server";
 import { renderApp } from "../test/render";
 import { UserMenu } from "./user-menu";
@@ -35,9 +35,13 @@ test("opens the menu showing email + role and signs out", async () => {
 });
 
 test("shows a pending state on Sign out while logging out", async () => {
+  let release!: () => void;
+  const gate = new Promise<void>((resolve) => {
+    release = resolve;
+  });
   server.use(
     http.post("/api/admin/logout", async () => {
-      await delay(50);
+      await gate;
       return new HttpResponse(null, { status: 204 });
     }),
   );
@@ -50,5 +54,10 @@ test("shows a pending state on Sign out while logging out", async () => {
   const menu = within(document.body);
   await userEvent.click(await menu.findByText("Sign out"));
 
+  // The logout is held open by `gate`, so the pending state is observed
+  // deterministically (no reliance on a timing window).
   expect(await menu.findByText(/signing out/i)).toBeInTheDocument();
+
+  release();
+  await waitFor(() => expect(menu.queryByText(/signing out/i)).toBeNull());
 });