fix(compare): give every basket entry a real phase

Review of the per-phase limit found entries reaching the basket with no
phase, and a phase-less entry holds a slot in both groups:

- Nearby-school cards added without one. The API now returns each
  peer's own phase (its pool is a phase group, so an all-through school
  can sit beside a primary); the button passes it through, and an older
  API simply leaves the conservative both-groups count in place.
- Baskets saved before this change were never migrated. The compare
  page now backfills missing phases from the data it already fetches,
  and never overwrites a phase the basket has.
- "16 plus" counted against both groups; it is secondary, as the API's
  PHASE_GROUPS files it.

Also rewraps the HomeView doc comment the previous commit left awkward.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

nextjs-app/lib/compareLogic.ts

@@ -309,7 +309,8 @@ export const MAX_PER_GROUP = 5;
 export function compareGroups(phase?: string | null): CompareGroup[] {
   const p = (phase ?? '').toLowerCase();
   // "Middle deemed secondary" / "Middle deemed primary" match here too.
-  if (p.includes('secondary')) return ['secondary'];
+  // "16 plus" is secondary, as the API's PHASE_GROUPS files it.
+  if (p.includes('secondary') || p === '16 plus') return ['secondary'];
   if (p.includes('primary')) return ['primary'];
   return ['primary', 'secondary'];
 }

nextjs-app/lib/types.ts

@@ -360,6 +360,8 @@ export interface NearbySchool {
   distance_miles: number;
   school_type: string | null;
   age_range: string | null;
+  /** Optional: a frontend can ship ahead of the API that serves it. */
+  phase?: string | null;
   shared: string[];
   metric_value: number | null;
   metric_key: string;