fix(school): address review on the header chip fixes

- E2E: list with page_size (per_page was ignored), fail clearly if the
  gender filter is ignored, and require nursery_provision on the detail
  payload so the Nursery assertion cannot pass vacuously.
- singleSexLabel ignores case, as hasNurseryClasses does.
- Header test: type withSchool with Partial<School>, and match the
  single-sex labels exactly instead of any span ending in "school".

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

e2e/tests/journeys.spec.ts

@@ -3293,11 +3293,14 @@ for (const width of [360, 390, 430]) {
  * school". Data-invariant: the chip follows whatever the API says.
  */
 test('a girls\' secondary header names it properly and shows Nursery only when it has one', async ({ page }) => {
-  const res = await page.request.get('/api/schools?search=school&phase=secondary&gender=girls&per_page=1');
+  const res = await page.request.get('/api/schools?search=school&phase=secondary&gender=girls&page_size=1');
   expect(res.ok()).toBeTruthy();
   const [school] = (await res.json()).schools ?? [];
   test.skip(!school, 'no girls\' secondary in this environment');
+  expect(school.gender, 'the gender filter was ignored').toBe('Girls');
   const detail = await (await page.request.get(`/api/schools/${school.urn}`)).json();
+  // Without the field, the Nursery assertion below would pass vacuously.
+  expect(detail.school_info).toHaveProperty('nursery_provision');
 
   await page.goto(`/school/${school.urn}`);
   const header = page.locator('header', { has: page.getByRole('heading', { level: 1 }) });