test(web-shell): wait for the restored card before clicking continue (#16286)

The nightly `web-shell Browser Regression` dies in the generated-UI
retention case at `expect.poll(() => text).toBeDefined()`: the click on
`#continue-analysis` produces no prompt request, so the capture route never
fires (run 41771749222, job 126382801964). The same case passes on a dev
machine — 6/6 runs here — so this is a host-timing shape, not a product
defect.

Wait for the card's continue control to be enabled, give dispatch a
CI-sized budget, and fail with the card and status state when nothing is
dispatched. The next nightly then names the cause instead of `undefined`.

packages/web-shell/client/e2e/generated-ui.retention.spec.ts

@@ -499,10 +499,32 @@ async function reviewSnapshot(page: Page, app: FrameLocator) {
     text = body.prompt[0].text;
     await route.fulfill({ status: 409, json: { error: 'captured by test' } });
   };
+  // A restored card finishes its first paint asynchronously, and a click that
+  // lands before the host accepts continuations is swallowed with no request
+  // and no error: the nightly run failed on the missing dispatch, not on the
+  // copy below. Wait for the button the app gates continuations on, then give
+  // dispatch a CI-sized budget so a loaded host is not read as a broken card.
+  await expect(app.locator('#continue-analysis')).toBeEnabled();
   await page.route('**/session/*/prompt', capture);
   try {
     await app.locator('#continue-analysis').click();
-    await expect.poll(() => text).toBeDefined();
+    const deadline = Date.now() + (process.env['CI'] ? 20_000 : 5_000);
+    while (!text && Date.now() < deadline) {
+      await page.waitForTimeout(100);
+    }
+    if (!text) {
+      const cardState = await app
+        .locator('#status')
+        .getAttribute('data-state')
+        .catch(() => null);
+      const status = await app
+        .locator('#continuation-status')
+        .textContent()
+        .catch(() => null);
+      throw new Error(
+        `continue never dispatched a prompt request (card=${cardState}, status=${status})`,
+      );
+    }
     await expect(app.locator('#continuation-status')).toContainText(
       'Not sent.',
     );