feat(search): one state school group, not academy and council-run

The School type filter split state schools into "academy or free
school" and "council-run". The two were near-halves of one pool (11,186
and 9,316 schools), so choosing one rarely narrowed anything, and the
split did not follow the difference a parent feels most, admissions:
voluntary aided and foundation schools set their own, as academies do.
Faith, which voluntary aided mostly meant, has its own filter.

They are now one group, "State school (free)", leaving five. The old
keys academy and council resolve to state, so a link made with them
keeps working instead of falling through to the raw-label path and
returning nothing.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

backend/school_groups.py

@@ -2,7 +2,7 @@
 
 The 34 GIAS establishment types describe governance and funding, which for a
 mainstream state school barely changes what a parent experiences. The search
-filter offers six groups a parent recognises instead, and a faith filter in
+filter offers five groups a parent recognises instead, and a faith filter in
 place of the faith signal that "Voluntary aided" and "Voluntary controlled"
 only half carry. See
 docs/superpowers/specs/2026-10-02-school-type-groups-and-faith-filter-design.md.
@@ -21,12 +21,16 @@ from .gias_codes import RELIGIOUS_CHARACTER, SCHOOL_TYPE
 
 # (key, label, GIAS TypeOfEstablishment codes), in the order shown.
 TYPE_GROUPS: tuple[tuple[str, str, frozenset[int]], ...] = (
-    # Academy sponsor led, Academy converter, Free schools, University technical
-    # college, Studio schools, City technology college. UTCs and studio schools
-    # are legally academies, and a family considering one searches by name.
-    ("academy", "State school: academy or free school", frozenset({28, 34, 35, 40, 41, 6})),
-    # Community, Voluntary aided, Voluntary controlled, Foundation, LA nursery.
-    ("council", "State school: council-run", frozenset({1, 2, 3, 5, 15})),
+    # Every mainstream state school, academy or council-run: Academy sponsor
+    # led, Academy converter, Free schools, University technical college,
+    # Studio schools, City technology college, Community, Voluntary aided,
+    # Voluntary controlled, Foundation, LA nursery. Academy against council-run
+    # was two near-halves of one pool, and did not follow the difference a
+    # parent feels most, admissions: voluntary aided and foundation schools
+    # set their own, as academies do. Faith, which voluntary aided mostly
+    # meant, has its own filter.
+    ("state", "State school (free)",
+     frozenset({28, 34, 35, 40, 41, 6, 1, 2, 3, 5, 15})),
     ("independent", "Independent (fee-paying)", frozenset({11})),
     # Every special type, independent ones included (usually funded by the
     # council through an EHCP, so SEND provision to a parent, not private
@@ -64,6 +68,10 @@ FAITH_GROUPS: tuple[tuple[str, str, frozenset[int]], ...] = (
 )
 
 TYPE_GROUP_KEYS: frozenset[str] = frozenset(k for k, _, _ in TYPE_GROUPS)
+
+# Keys a group was offered under before, so their links keep working: "state"
+# was "academy" and "council" until 2026-10-02.
+TYPE_GROUP_ALIASES: dict[str, str] = {"academy": "state", "council": "state"}
 FAITH_KEYS: frozenset[str] = frozenset(k for k, _, _ in FAITH_GROUPS)
 
 
@@ -86,6 +94,14 @@ for _faith, _, _codes in FAITH_GROUPS:
             _FAITHS_BY_NAME[_name] = _FAITHS_BY_NAME.get(_name, ()) + (_faith,)
 
 
+def type_group_key(value: str) -> Optional[str]:
+    """The type group a school_type URL value names, old keys included, or
+    None when it names no group (an old link's raw GIAS type)."""
+    v = value.strip().lower()
+    v = TYPE_GROUP_ALIASES.get(v, v)
+    return v if v in TYPE_GROUP_KEYS else None
+
+
 def type_group_for(name: object) -> Optional[str]:
     """The type group of a GIAS establishment type name, or None."""
     if not isinstance(name, str):