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/HomeView.tsx

@@ -150,10 +150,11 @@ interface ValueProp {
  *
  * Every claim here must name something the product actually does. Two of the
  * four previously did not: "up to three schools" contradicted the basket limit
- * (now MAX_PER_GROUP = 5 per phase, in lib/compareLogic.ts) (and the card further down the page, which
- * correctly said five), and "class sizes" described data the codebase has never
- * held — grep for it and this line was the only hit. Both are corrected below
- * against the real fields, which live in components/school/InclusionSection.tsx.
+ * of five (and the card further down the page, which correctly said five), and
+ * "class sizes" described data the codebase has never held — grep for it and
+ * this line was the only hit. Both are corrected below against the real
+ * fields, which live in components/school/InclusionSection.tsx.
+ * The limit is now five per phase: MAX_PER_GROUP in lib/compareLogic.ts.
  */
 const VALUE_PROPS: ValueProp[] = [
   {