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__/lib/utils.test.ts

@@ -366,6 +366,11 @@ describe('singleSexLabel', () => {
     expect(singleSexLabel('Boys')).toBe("Boys' school");
   });
 
+  it('ignores case, as hasNurseryClasses does', () => {
+    expect(singleSexLabel(' girls ')).toBe("Girls' school");
+    expect(singleSexLabel('BOYS')).toBe("Boys' school");
+  });
+
   it('returns null for a mixed or unknown school', () => {
     expect(singleSexLabel('Mixed')).toBeNull();
     expect(singleSexLabel(null)).toBeNull();