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/components/school/SecondaryAdmissionsSection.tsx

@@ -7,7 +7,7 @@
  */
 
 import type { School, SchoolAdmissions, SchoolAdmissionDistance } from '@/lib/types';
-import { formatPercentage } from '@/lib/utils';
+import { formatPercentage, hasReligiousCharacter, isSelective } from '@/lib/utils';
 import { Section, sectionStyles as styles } from './sectionShared';
 import {
   describeCutoff, describeCutoffAbsence,
@@ -33,10 +33,8 @@ export function SecondaryAdmissionsSection({
   const featureOn = admissionDistance !== undefined;
   // Moved with this section from SecondarySchoolDetailView, its only consumer.
   const admissionsTag = (() => {
-    const policy = schoolInfo.admissions_policy?.toLowerCase() ?? '';
-    if (policy.includes('selective')) return 'Selective';
-    const denom = schoolInfo.religious_denomination ?? '';
-    if (denom && denom !== 'Does not apply') return 'Faith priority';
+    if (isSelective(schoolInfo.admissions_policy)) return 'Selective';
+    if (hasReligiousCharacter(schoolInfo.religious_denomination)) return 'Faith priority';
     return null;
   })();