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>

backend/nearby_schools.py

@@ -250,6 +250,10 @@ def select_nearby(frame: pd.DataFrame, urn: int) -> list[dict]:
             "distance_miles": float(row["distance_miles"]),
             "school_type": _native(row.get("school_type")),
             "age_range": _native(row.get("age_range")),
+            # Each peer's own phase, not the subject's: the pool is a phase
+            # group, so an all-through school can sit beside a primary. The
+            # compare basket counts it against both of its tabs.
+            "phase": _native(row.get("phase")),
             "shared": _shared(subject, row, is_secondary),
             "metric_value": _native(row.get(metric_key)),
             "metric_key": metric_key,

backend/tests/test_nearby_schools.py

@@ -163,6 +163,18 @@ def test_secondary_reaches_further_than_primary():
     assert {s["urn"] for s in select_nearby(frame, 100001)} == {100002, 100003}
 
 
+def test_each_card_carries_its_own_phase():
+    # The compare basket limits each phase separately, so an all-through peer
+    # must not inherit the subject's "Primary".
+    frame = _frame(
+        _row(100001, "Subject"),
+        _row(100002, "A", latitude=_at(0.5)),
+        _row(100003, "B", phase="All-through", age_range="4-18", latitude=_at(0.6)),
+    )
+    phases = {s["urn"]: s["phase"] for s in select_nearby(frame, 100001)}
+    assert phases == {100002: "Primary", 100003: "All-through"}
+
+
 def test_the_cap_follows_the_phase():
     assert radius_miles("Primary") == 2.0
     assert radius_miles("Middle deemed primary") == 2.0