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/components/school/PrimarySchoolSections.tsx

@@ -155,7 +155,7 @@ export function PrimarySchoolSections({
       <SimilarSchoolsSection
         urn={schoolInfo.urn}
         schoolName={schoolInfo.school_name}
-        phaseNoun={flags.isAllThrough ? 'all-through' : 'primary'}
+        phase={schoolInfo.phase}
         thisMetricValue={flags.latestResults?.rwm_expected_pct ?? null}
         similar={similarSchools}
       />

nextjs-app/components/school/SecondarySchoolSections.tsx

@@ -149,7 +149,7 @@ export function SecondarySchoolSections({
       <SimilarSchoolsSection
         urn={schoolInfo.urn}
         schoolName={schoolInfo.school_name}
-        phaseNoun="secondary"
+        phase={schoolInfo.phase}
         thisMetricValue={flags.latestResults?.attainment_8_score ?? null}
         similar={similarSchools}
       />

nextjs-app/components/school/SimilarSchoolsSection.tsx

@@ -28,6 +28,28 @@ export function shouldRenderSimilar(similar?: SimilarSchool[] | null): boolean {
   return (similar?.length ?? 0) >= MINIMUM;
 }
 
+/**
+ * What the lede calls the set of schools it is showing.
+ *
+ * Derived from the school's own GIAS phase rather than the template it renders
+ * with, because those disagree for "16 plus" (GIAS phase 6): a sixth-form
+ * college renders the primary template — computeSchoolFlags tests for the
+ * substring "secondary" — while the backend correctly matches it against the
+ * secondary group. Taking the noun from the template would print "Other primary
+ * schools near <sixth form college>" above a row of secondaries.
+ *
+ * A 16-plus school's candidates span the whole secondary group, so no single
+ * noun fits and it gets the honest general one.
+ */
+export function nearbyNoun(phase: string | null | undefined): string {
+  const text = (phase ?? '').trim().toLowerCase();
+  if (text === 'all-through') return 'all-through schools';
+  if (text === '16 plus') return 'schools and colleges';
+  if (text.includes('secondary')) return 'secondary schools';
+  if (text.includes('primary')) return 'primary schools';
+  return 'schools';
+}
+
 function metricLabel(key: string): string {
   return key === 'attainment_8_score' ? 'Attainment 8' : 'Reading, writing & maths';
 }
@@ -40,13 +62,14 @@ function formatMetric(value: number | null, key: string): string {
 export function SimilarSchoolsSection({
   urn,
   schoolName,
-  phaseNoun,
+  phase,
   thisMetricValue,
   similar,
 }: {
   urn: number;
   schoolName: string;
-  phaseNoun: string;
+  /** The school's own GIAS phase, not the template it renders with. */
+  phase: string | null | undefined;
   thisMetricValue: number | null;
   similar?: SimilarSchool[] | null;
 }) {
@@ -57,6 +80,7 @@ export function SimilarSchoolsSection({
   // shares an intake with this school.
   const loosest = Math.max(...schools.map((s) => s.tier));
   const metricKey = schools[0].metric_key;
+  const noun = nearbyNoun(phase);
 
   return (
     <Section id="similar">
@@ -70,8 +94,8 @@ export function SimilarSchoolsSection({
             </h2>
             <p className={styles.lede}>
               {loosest >= 3
-                ? `Other ${phaseNoun} schools near ${schoolName}.`
-                : `Other ${phaseNoun} schools near ${schoolName}, with a similar intake.`}
+                ? `Other ${noun} near ${schoolName}.`
+                : `Other ${noun} near ${schoolName}, with a similar intake.`}
             </p>
           </div>
         }