fix(school): send the school page its admissions policy, and read it exactly

The header's Selective flag read school_info.admissions_policy, which the
detail endpoint never sent, so no school page could flag Selective while
its search row did (staging E2E: The Grammar School at Leeds). The detail
payload now carries it, and a contract test checks it carries every field
the header's flags read.

Sending it would have switched on two older copies of the tag logic #176
fixed in the rows. The Admissions section and the cut-off note both tested
includes('selective'), so every non-selective secondary would have read
"entry is by selective examination". The section also counted "None" as a
faith: Burntwood reads "a faith-based admissions priority (None)" today.
All of them now share isSelective() and hasReligiousCharacter(), which also
treats "Not applicable" as no faith, as the place table already does.

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

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

@@ -0,0 +1,58 @@
+/**
+ * The Admissions section's Selective and faith notes.
+ *
+ * It tested the policy with includes('selective'), which "Non-selective"
+ * passes, and excluded only "Does not apply" from the religious character, so
+ * Burntwood (no religious character, recorded as "None") read "this school
+ * has a faith-based admissions priority (None)". The Selective half never
+ * fired only because the school page's API did not send admissions_policy.
+ */
+
+import { screen, within } from '@testing-library/react';
+import type { School } from '@/lib/types';
+import { secondaryFixture } from '../support/schoolFixtures';
+import { renderSecondarySchoolDetail } from '../support/renderSchoolDetail';
+
+jest.mock('@/lib/analytics', () => ({
+  track: jest.fn(),
+  getNavigationSource: () => 'direct',
+}));
+jest.mock('@/components/PerformanceChart', () => ({
+  PerformanceChart: () => <div data-testid="performance-chart" />,
+}));
+jest.mock('@/components/AdmissionsTrendChart', () => ({
+  __esModule: true,
+  default: () => <div data-testid="admissions-trend-chart" />,
+}));
+jest.mock('@/components/SchoolHeroMap', () => ({
+  SchoolHeroMap: () => <div data-testid="hero-map" />,
+  __esModule: true,
+}));
+
+function admissionsOf(info: Partial<School>) {
+  renderSecondarySchoolDetail({ ...secondaryFixture, schoolInfo: { ...secondaryFixture.schoolInfo, ...info } });
+  return within(screen.getByRole('heading', { name: 'Admissions' }).closest('section')!);
+}
+
+describe('Admissions section notes', () => {
+  it('notes the entrance test for a selective school', () => {
+    const section = admissionsOf({ admissions_policy: 'Selective', religious_denomination: 'None' });
+    expect(section.getByText('Selective:')).toBeInTheDocument();
+  });
+
+  it('does not call a non-selective school selective', () => {
+    const section = admissionsOf({ admissions_policy: 'Non-selective', religious_denomination: 'None' });
+    expect(section.queryByText('Selective:')).not.toBeInTheDocument();
+  });
+
+  it.each(['None', 'Does not apply'])('claims no faith priority when the register says %p', (religious_denomination) => {
+    // Not "Non-selective": a misread Selective would win and hide this case.
+    const section = admissionsOf({ admissions_policy: 'Not applicable', religious_denomination });
+    expect(section.queryByText('Faith priority:')).not.toBeInTheDocument();
+  });
+
+  it('notes the religious character of a faith school', () => {
+    const section = admissionsOf({ admissions_policy: 'Non-selective', religious_denomination: 'Church of England' });
+    expect(section.getByText('Faith priority:')).toBeInTheDocument();
+  });
+});