fix(admissions): flag-off pages must not speak for the council

The secondary admissions section words the absence of a cut-off distance:
"<LA> has not published a cut-off distance for this school." That sentence
is true when the authority publishes nothing. It is false when the
authority does publish and the admission_distance flag is simply off — and
off is the current state, so every secondary page with an EES admissions
row has been making a claim about a council on our behalf.

The backend already draws the distinction the copy needs. /api/schools/{urn}
omits the admission_distance key entirely while the flag is dark rather than
sending null, precisely so that "we are not publishing cut-offs" stays
distinguishable from "this school has no cut-off"; lib/types.ts says so in
as many words. The page then collapsed the two with `?? null` before the
section ever saw them.

So stop collapsing it: thread the raw field to SecondarySchoolSections and
word the absence only when the feature is on. Null still gets the sentence
naming the authority — that case is unchanged and still tested.

Primary pages are unaffected: AdmissionsSection carries no absence copy and
renders nothing when there is no figure. DistanceSection already treated
absent and null alike; only its type widens.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01FuPUioHpxtaiDNagQvjxyM

nextjs-app/components/school/DistanceSection.tsx

@@ -24,7 +24,7 @@ export function DistanceSection({
   admissionDistance,
   schoolInfo,
 }: {
-  admissionDistance: SchoolAdmissionDistance | null;
+  admissionDistance: SchoolAdmissionDistance | null | undefined;
   schoolInfo: School;
 }) {
   // Without a figure there is nothing to compare against, and without

nextjs-app/components/school/SecondaryAdmissionsSection.tsx

@@ -21,11 +21,17 @@ export function SecondaryAdmissionsSection({
      published cut-off and no EES admissions row. */
   admissions: SchoolAdmissions | null;
   admissionsHistory: SchoolAdmissions[];
-  admissionDistance: SchoolAdmissionDistance | null;
+  admissionDistance: SchoolAdmissionDistance | null | undefined;
   schoolInfo: School;
   hasSixthForm: boolean;
 }) {
   const cutoff = describeCutoff(admissionDistance);
+  /* Absent means cut-offs are not being published at all; null means this
+     school has no published cut-off. Only the second is a fact about the
+     school, and only the second can be stated. Saying "X has not published a
+     cut-off" while the feature is dark describes us, and is false wherever the
+     authority does publish one. */
+  const featureOn = admissionDistance !== undefined;
   // Moved with this section from SecondarySchoolDetailView, its only consumer.
   const admissionsTag = (() => {
     const policy = schoolInfo.admissions_policy?.toLowerCase() ?? '';
@@ -102,7 +108,7 @@ export function SecondaryAdmissionsSection({
           {CUTOFF_NOTE} {CUTOFF_MEASUREMENT_NOTE}
           {cutoff.routeNote && <> {cutoff.routeNote}</>}
         </p>
-      ) : (
+      ) : featureOn ? (
         <p className={styles.sectionSubtitle} style={{ marginTop: '1rem' }}>
           {describeCutoffAbsence({
             localAuthority: schoolInfo.local_authority,
@@ -110,7 +116,7 @@ export function SecondaryAdmissionsSection({
             admissionsHistory,
           })}
         </p>
-      )}
+      ) : null}
 
       {hasSixthForm && (
         <div className={styles.sixthFormNote}>

nextjs-app/components/school/SecondarySchoolSections.tsx

@@ -36,7 +36,10 @@ export interface SecondarySchoolSectionsProps {
   /** Needed to tell a year with no published cut-off apart from a year the
    *  school simply was not oversubscribed. */
   admissionsHistory: SchoolAdmissions[];
-  admissionDistance: SchoolAdmissionDistance | null;
+  /** Absent — not null — while the admission_distance flag is off. The two
+   *  mean different things to the reader and must stay distinguishable:
+   *  see SecondaryAdmissionsSection, which words the absence. */
+  admissionDistance: SchoolAdmissionDistance | null | undefined;
   deprivation: SchoolDeprivation | null;
   finance: SchoolFinance | null;
   nationalAvg: NationalAverages | null;