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/__tests__/context/ComparisonProvider.test.tsx

@@ -0,0 +1,114 @@
+/**
+ * The basket limit is five per phase group, not five overall, and the
+ * provider is where it is enforced for every add path.
+ *
+ * Entries without a phase count against both groups. Baskets saved before
+ * phases were recorded hold such entries, so the compare page backfills them
+ * once it has fetched each school.
+ */
+
+import { act, render, screen, fireEvent } from '@testing-library/react';
+
+import { AddToCompareButton } from '@/components/school/AddToCompareButton';
+import { ComparisonProvider } from '@/context/ComparisonProvider';
+import { useComparisonContext } from '@/context/ComparisonContext';
+import type { NearbySchool, School } from '@/lib/types';
+
+type Ctx = ReturnType<typeof useComparisonContext>;
+
+function renderBasket(stored: Partial<School>[] = []) {
+  window.localStorage.setItem('selectedSchools', JSON.stringify(stored));
+  const ref: { current: Ctx | null } = { current: null };
+  function Probe() {
+    ref.current = useComparisonContext();
+    return null;
+  }
+  render(
+    <ComparisonProvider>
+      <Probe />
+    </ComparisonProvider>,
+  );
+  return ref as { current: Ctx };
+}
+
+const school = (urn: number, phase: string | null) =>
+  ({ urn, school_name: `School ${urn}`, phase }) as School;
+
+beforeEach(() => {
+  window.localStorage.clear();
+  jest.spyOn(window, 'alert').mockImplementation(() => {});
+});
+
+afterEach(() => jest.restoreAllMocks());
+
+it('holds five primary and five secondary schools, and no more of either', () => {
+  const ctx = renderBasket();
+  act(() => {
+    for (let i = 0; i < 6; i++) ctx.current.addSchool(school(100000 + i, 'Primary'));
+    for (let i = 0; i < 6; i++) ctx.current.addSchool(school(200000 + i, 'Secondary'));
+  });
+  expect(ctx.current.selectedSchools).toHaveLength(10);
+  expect(window.alert).toHaveBeenCalledWith(expect.stringMatching(/5 primary schools/));
+  expect(window.alert).toHaveBeenCalledWith(expect.stringMatching(/5 secondary schools/));
+});
+
+it('frees the second group once a stored entry learns its phase', () => {
+  // Three phase-less entries from an older basket plus two primaries: the
+  // primary group reads as full although only two are really primary.
+  const ctx = renderBasket([
+    school(100001, null),
+    school(100002, null),
+    school(100003, null),
+    school(100004, 'Primary'),
+    school(100005, 'Primary'),
+  ]);
+  expect(ctx.current.fullGroupFor({ phase: 'Primary' })).toBe('primary');
+
+  act(() => {
+    ctx.current.backfillPhases({ 100001: 'Secondary', 100002: 'Secondary', 100003: 'Secondary' });
+  });
+
+  expect(ctx.current.fullGroupFor({ phase: 'Primary' })).toBeNull();
+  expect(ctx.current.selectedSchools.map((s) => s.phase)).toEqual([
+    'Secondary',
+    'Secondary',
+    'Secondary',
+    'Primary',
+    'Primary',
+  ]);
+});
+
+it('never overwrites a phase the basket already has', () => {
+  const ctx = renderBasket([school(100001, 'Primary')]);
+  act(() => ctx.current.backfillPhases({ 100001: 'All-through' }));
+  expect(ctx.current.selectedSchools[0].phase).toBe('Primary');
+});
+
+it('a nearby card adds its own phase, not an unknown one', () => {
+  const nearby = {
+    urn: 100009,
+    school_name: 'Nearby',
+    distance_miles: 0.4,
+    school_type: 'Academy',
+    age_range: '4-18',
+    phase: 'All-through',
+    shared: [],
+    metric_value: null,
+    metric_key: 'rwm_expected_pct',
+    metric_year: null,
+  } as NearbySchool;
+
+  const ref: { current: Ctx | null } = { current: null };
+  function Probe() {
+    ref.current = useComparisonContext();
+    return null;
+  }
+  render(
+    <ComparisonProvider>
+      <Probe />
+      <AddToCompareButton school={nearby} />
+    </ComparisonProvider>,
+  );
+  fireEvent.click(screen.getByRole('button', { name: /Add to compare/ }));
+  expect(ref.current?.selectedSchools[0].phase).toBe('All-through');
+});

nextjs-app/__tests__/lib/compareLogic.test.ts

@@ -328,6 +328,7 @@ describe('basket limits per comparison group', () => {
     expect(compareGroups('Middle deemed primary')).toEqual(['primary']);
     expect(compareGroups('Secondary')).toEqual(['secondary']);
     expect(compareGroups('Middle deemed secondary')).toEqual(['secondary']);
+    expect(compareGroups('16 plus')).toEqual(['secondary']);
   });
 
   it('counts schools that could land in either tab against both', () => {