fix(web-app-docs): assert the yaml page on the tree the run deployed

The spec asserted /latest/compose.html. latest is the released tag built
from the git mirror, so no working-tree change can ever reach it; deployed
is the unlisted version built from the tree under test. Pointing the spec at
deployed makes it fail for a broken tree instead of passing on a stale one.

That move changes what the readiness gate has to wait for. There is no
version-state entry for deployed, so the poll now asks the page itself for a
200, and that request is what triggers the on-demand Sphinx build. The
budgets follow test-languages.js, which already waits for the same build:
50 minutes for the test, 45 for the poll, probed every 30 seconds instead of
continuously. The previous pairing could not work in either mode. Without a
per-test override the config allows 300000 ms, exactly the old poll budget,
so the test was killed at the instant the poll was due to report; on an
onion target resolveTimeout scales the poll to 25 minutes against a 15
minute test budget.

The poll also had to survive a refused connection. The server refuses while
it builds, and a callback that throws ends expect.poll rather than retrying
it, so the first refusal failed the test outright.

The heading is matched by prefix because docutils appends its permalink
pilcrow as a bare text node. The theme hides `.headerlink > *`, which
matches no element, so the accessible name is `compose.yml¶` and an exact
match can never succeed.

On-demand builds of the deployed tree are why three specs in this role carry
a timeout far above the suite default; each names the build it waits for.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

roles/web-app-docs/files/playwright/test-yaml-page.js

@@ -2,26 +2,41 @@ const { test, expect } = require("@playwright/test");
 const { resolveTimeout } = require("./timeouts");
 const { gotoOnion } = require("./personas");
 
-const YAML_PAGE = "/latest/compose.html";
+const YAML_PAGE = "/deployed/compose.html";
 const FIRST_KEY = "x-ci-defaults";
 const LATER_KEY = "dns_opt";
 
 exports.register = function (shared) {
   test("a yaml source page shows the file as one highlighted block", async ({ page, request }) => {
+    test.setTimeout(resolveTimeout(3_000_000)); // the English Sphinx build of the deployed working tree
     await expect
-      .poll(() => shared.versionState(request, "latest"), {
-        message: "Expected the latest site to finish building before its pages are asserted",
-        timeout: resolveTimeout(300_000),
+      .poll(async () => {
+        try {
+          const response = await request.get(`${shared.appBaseUrl}${YAML_PAGE}`, {
+            failOnStatusCode: false,
+            timeout: resolveTimeout(30_000),
+          });
+          return response.status();
+        } catch {
+          return 0; // the server refuses connections while it builds; a throw would end the poll
+        }
+      }, {
+        message: "Expected the deployed YAML page to finish building before it is asserted",
+        timeout: resolveTimeout(2_700_000),
+        intervals: [30_000],
       })
-      .toBe("ready");
+      .toBe(200);
 
     const response = await gotoOnion(page, `${shared.appBaseUrl}${YAML_PAGE}`);
     expect(response, `Expected a response for ${YAML_PAGE}`).toBeTruthy();
     expect(response.status(), `Expected ${YAML_PAGE} to be served`).toBe(200);
 
     await expect(
-      page.getByRole("heading", { name: "compose.yml", exact: true }),
-      "Expected the page to be titled after the file, which the yaml parser supplies",
+      page.getByRole("heading", { name: /^compose\.yml/ }),
+      "Expected the page to be titled after the file, which the yaml parser supplies. " +
+        "The name is matched by prefix because docutils appends its permalink pilcrow as a " +
+        "bare text node, which the theme hides through `.headerlink > *` and therefore never " +
+        "hides at all, so the accessible name is `compose.yml¶`",
     ).toBeVisible({ timeout: resolveTimeout(30_000) });
 
     const block = page.locator("div.highlight-yaml pre");