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/context/ComparisonContext.tsx

@@ -17,6 +17,8 @@ interface ComparisonContextType {
   addSchool: (school: School) => void;
   removeSchool: (urn: number) => void;
   replaceSchools: (schools: School[]) => void;
+  /** Fill in phases missing from stored entries; never overwrites one. */
+  backfillPhases: (phases: Record<number, string | null | undefined>) => void;
   clearAll: () => void;
   isSelected: (urn: number) => boolean;
   /** The comparison group with no room for this school, or null. */