fix(api): treat "16 plus" as secondary, the way PHASE_GROUPS already does

GIAS phase 6 is "16 plus", and PHASE_GROUPS deliberately files it in the
secondary group. The payload helper decided the same question with
`"secondary" in phase_text`, which that value does not satisfy — so a
sixth-form college was handed the primary bucket and offered infant schools
as its peers, with the KS2 metric key to label them. No crash; just a page
confidently showing the wrong schools.

The decision now lives in similar_schools.is_secondary_phase, beside the
PHASE_GROUPS bucket it selects from, so the two cannot drift again. A test
pins them together.

The same binary assumption had a second output. computeSchoolFlags tests for
the substring too, so a 16-plus school renders the primary template, and the
composer was labelling the section from the template: "Other primary schools
near <sixth form college>" above a row of secondaries. The section now
derives its noun from the school's own phase, which also removes the
duplicated wording from both composers. A 16-plus school's candidates span
the whole secondary group, so no single noun fits and it gets the honest
general one.

Reported in review on #150.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

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

@@ -8,6 +8,7 @@
 import { render, screen } from '@testing-library/react';
 
 import {
+  nearbyNoun,
   SimilarSchoolsSection,
   shouldRenderSimilar,
 } from '@/components/school/SimilarSchoolsSection';
@@ -46,7 +47,7 @@ function renderSection(similar: SimilarSchool[]) {
     <SimilarSchoolsSection
       urn={100001}
       schoolName="Meadowbrook Primary School"
-      phaseNoun="primary"
+      phase="Primary"
       thisMetricValue={72}
       similar={similar}
     />,
@@ -85,6 +86,37 @@ describe('the claim the lede makes', () => {
   });
 });
 
+describe('what the lede calls the set', () => {
+  it.each([
+    ['Primary', 'primary schools'],
+    ['Middle deemed primary', 'primary schools'],
+    ['Secondary', 'secondary schools'],
+    ['Middle deemed secondary', 'secondary schools'],
+    ['All-through', 'all-through schools'],
+    // GIAS phase 6. Its candidates span the whole secondary group, so no
+    // single noun fits and it takes the honest general one.
+    ['16 plus', 'schools and colleges'],
+    ['', 'schools'],
+    [null, 'schools'],
+  ])('calls a %s school\'s neighbours "%s"', (phase, expected) => {
+    expect(nearbyNoun(phase)).toBe(expected);
+  });
+
+  it('never calls a sixth form college\'s neighbours primary schools', () => {
+    render(
+      <SimilarSchoolsSection
+        urn={100001}
+        schoolName="Barnet Sixth Form College"
+        phase="16 plus"
+        thisMetricValue={null}
+        similar={[school(), school({ urn: 100003 })]}
+      />,
+    );
+    expect(screen.getByText(/Other schools and colleges near Barnet Sixth Form College/)).toBeInTheDocument();
+    expect(screen.queryByText(/primary schools/)).not.toBeInTheDocument();
+  });
+});
+
 describe('cards', () => {
   it('links each school to its canonical slug', () => {
     renderSection([school(), school({ urn: 100003, school_name: 'Oakfield Primary School' })]);