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/components/school/AddToCompareButton.tsx

@@ -28,6 +28,9 @@ export function AddToCompareButton({ school }: { school: NearbySchool }) {
       school_name: school.school_name,
       school_type: school.school_type,
       age_range: school.age_range,
+      // The basket limits each phase separately. Missing (an older API)
+      // counts against both groups, which is safe, just stricter.
+      phase: school.phase ?? null,
     } as School);
   };