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__/lib/lastDistanceOffered.test.ts

@@ -157,6 +157,13 @@ describe('compareToCutoff', () => {
 });
 
 describe('describeCutoffAbsence', () => {
+  it('does not read "Non-selective" as selective', () => {
+    // A substring test matched "selective" inside "Non-selective".
+    const s = describeCutoffAbsence({ localAuthority: 'Wandsworth', admissionsPolicy: 'Non-selective' });
+    expect(s).not.toMatch(/entrance test/);
+    expect(s).toMatch(/^Wandsworth has not published/);
+  });
+
   it('explains a selective school by how it admits, not as missing data', () => {
     const s = describeCutoffAbsence({ localAuthority: 'Kent', admissionsPolicy: 'Selective' });
     expect(s).toContain('entrance test');