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/ComparisonView.tsx

@@ -53,7 +53,8 @@ export function ComparisonView({
   const router = useRouter();
   const pathname = usePathname();
   const searchParams = useSearchParams();
-  const { selectedSchools, removeSchool, replaceSchools, isInitialized } = useComparison();
+  const { selectedSchools, removeSchool, replaceSchools, backfillPhases, isInitialized } =
+    useComparison();
 
   const [selectedMetric, setSelectedMetric] = useState(initialMetric);
   const [isModalOpen, setIsModalOpen] = useState(false);
@@ -157,6 +158,17 @@ export function ComparisonView({
     };
   }, [urnKey, isInitialized]);
 
+  useEffect(() => {
+    if (!comparisonData) return;
+    backfillPhases(
+      Object.fromEntries(
+        Object.values(comparisonData)
+          .filter((d) => d?.school_info)
+          .map((d) => [d.school_info.urn, d.school_info.phase]),
+      ),
+    );
+  }, [comparisonData, backfillPhases]);
+
   const primarySchools = selectedSchools.filter((school) => {
     const info = comparisonData?.[school.urn]?.school_info;
     const hasPrimaryData =

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[] = [
   {

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);
   };