feat(api): decide which nearby schools a page may offer

Hard filters encode claims the section may not make — a selective school is
not an alternative to a non-selective one, a special school is not comparable
to a mainstream one, a Girls school is not an option for a Boys school's
reader — so they never relax. Soft preferences describe closeness of fit, so
they relax across three tiers, and only far enough to reach three; the
remaining slots up to six fill from the tiers already opened.

PHASE_GROUPS moves to schemas.py so this module can share it without
importing app, which would be a cycle.

_mask() exists because Series.apply on an empty Series returns a DataFrame,
and using that as a mask drops every column — so the next lookup raises
KeyError instead of yielding no rows. A special school with no special school
near it empties the frame at the provision filter, which is the ordinary case
for most special schools, so this was a crash on a common path rather than an
edge case.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

backend/schemas.py

@@ -532,6 +532,18 @@ RANKING_COLUMNS = [
     "gcse_grade_91_pct",
 ]
 
+# Maps user-facing phase filter values to the GIAS PhaseOfEducation values they
+# include. All-through schools appear in both primary and secondary results,
+# which is why this is a set per phase rather than a single string comparison.
+#
+# Lives here rather than in app.py because similar_schools.py needs it too, and
+# importing app from there would be a cycle.
+PHASE_GROUPS: dict[str, set[str]] = {
+    "primary": {"primary", "middle deemed primary", "all-through"},
+    "secondary": {"secondary", "middle deemed secondary", "all-through", "16 plus"},
+    "all-through": {"all-through"},
+}
+
 # School listing columns
 SCHOOL_COLUMNS = [
     "urn",