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>

nextjs-app/__tests__/components/schoolDetailHeader.test.tsx

@@ -7,6 +7,7 @@
  */
 
 import { screen } from '@testing-library/react';
+import type { School } from '@/lib/types';
 import { primaryFixture, secondaryFixture } from '../support/schoolFixtures';
 import { renderSchoolDetail, renderSecondarySchoolDetail } from '../support/renderSchoolDetail';
 
@@ -30,7 +31,7 @@ jest.mock('@/components/SchoolHeroMap', () => ({
   __esModule: true,
 }));
 
-function withSchool<T extends { schoolInfo: object }>(fixture: T, info: object): T {
+function withSchool<T extends { schoolInfo: School }>(fixture: T, info: Partial<School>): T {
   return { ...fixture, schoolInfo: { ...fixture.schoolInfo, ...info } };
 }
 
@@ -61,6 +62,6 @@ describe('school header single-sex chip', () => {
 
   it('says nothing for a mixed school', () => {
     renderSecondarySchoolDetail(withSchool(secondaryFixture, { gender: 'Mixed' }));
-    expect(screen.queryByText(/school$/, { selector: 'span' })).not.toBeInTheDocument();
+    expect(screen.queryByText(/^(Girls|Boys|Mixed)'s? school$/)).not.toBeInTheDocument();
   });
 });