fix(admissions): flag-off pages must not speak for the council

The secondary admissions section words the absence of a cut-off distance:
"<LA> has not published a cut-off distance for this school." That sentence
is true when the authority publishes nothing. It is false when the
authority does publish and the admission_distance flag is simply off — and
off is the current state, so every secondary page with an EES admissions
row has been making a claim about a council on our behalf.

The backend already draws the distinction the copy needs. /api/schools/{urn}
omits the admission_distance key entirely while the flag is dark rather than
sending null, precisely so that "we are not publishing cut-offs" stays
distinguishable from "this school has no cut-off"; lib/types.ts says so in
as many words. The page then collapsed the two with `?? null` before the
section ever saw them.

So stop collapsing it: thread the raw field to SecondarySchoolSections and
word the absence only when the feature is on. Null still gets the sentence
naming the authority — that case is unchanged and still tested.

Primary pages are unaffected: AdmissionsSection carries no absence copy and
renders nothing when there is no figure. DistanceSection already treated
absent and null alike; only its type widens.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FuPUioHpxtaiDNagQvjxyM

e2e/tests/journeys.spec.ts

@@ -1304,6 +1304,52 @@ test('with the distance feature off, the section is absent rather than empty', a
     .toHaveCount(0);
 });
 
+/**
+ * A secondary school carrying an EES admissions row, which is what makes its
+ * Admissions section render while the distance feature is dark.
+ */
+async function secondarySchoolWithAdmissions(page: Page) {
+  const list = await page.request.get('/api/schools?phase=secondary&page_size=40');
+  if (!list.ok()) return null;
+  const body = await list.json();
+  for (const s of (body?.schools ?? []).slice(0, 25)) {
+    const res = await page.request.get(`/api/schools/${s.urn}`);
+    if (!res.ok()) continue;
+    const detail = await res.json();
+    if (detail?.admissions == null) continue;
+    return { urn: s.urn as number };
+  }
+  return null;
+}
+
+test('with the distance feature off, a secondary page makes no claim about publication', async ({ page }) => {
+  /*
+   * Shipping dark must not put words in the council's mouth. The secondary
+   * template is the only one that words the absence, and "X has not published
+   * a cut-off distance for this school" is false wherever X does publish and
+   * we are simply withholding it.
+   *
+   * This is why the API omits the key rather than sending null: absent means
+   * "cut-offs are not published at all", null means "this school has none".
+   * Only the second is a fact about the school, and only the second is sayable.
+   */
+  test.skip(await distanceFeatureIsOn(page),
+    'the admission_distance flag is on in this environment');
+
+  const found = await secondarySchoolWithAdmissions(page);
+  test.skip(found === null, 'no secondary school in the sample has an admissions row');
+
+  await page.goto(`/school/${found!.urn}`);
+  await expect(page.locator('h1').first()).toBeVisible({ timeout: 15_000 });
+
+  // The Admissions section is still there — this is not a test that the whole
+  // section vanished, which would pass for the wrong reason.
+  await expect(page.locator('#admissions')).toHaveCount(1);
+
+  await expect(page.getByText(/has not published a cut-off distance/)).toHaveCount(0);
+  await expect(page.getByText(/Contact the admissions authority/)).toHaveCount(0);
+});
+
 test('/api/flags is not reachable from the public internet', async ({ page }) => {
   // It names every unreleased feature and whether it is on. Next reads it
   // server-side over the Docker network; the public proxy must deny it.