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/tests/test_school_groups.py

@@ -17,6 +17,7 @@ from backend.school_groups import (
     UNOFFERED_TYPE_CODES,
     faith_groups_for,
     type_group_for,
+    type_group_key,
 )
 
 DBT_PROJECT = Path(__file__).resolve().parents[2] / "pipeline" / "transform" / "dbt_project.yml"
@@ -40,7 +41,7 @@ def test_every_religion_code_has_a_faith():
 
 def test_type_groups_in_display_order():
     assert [k for k, _, _ in TYPE_GROUPS] == [
-        "academy", "council", "independent", "special", "post16", "alternative"]
+        "state", "independent", "special", "post16", "alternative"]
 
 
 def test_faiths_in_display_order():
@@ -50,21 +51,34 @@ def test_faiths_in_display_order():
 
 
 @pytest.mark.parametrize("name, group", [
-    ("Academy converter", "academy"),
-    ("University technical college", "academy"),
-    ("Voluntary aided school", "council"),
-    ("Local authority nursery school", "council"),
+    ("Academy converter", "state"),
+    ("University technical college", "state"),
+    ("Voluntary aided school", "state"),
+    ("Local authority nursery school", "state"),
     ("Other independent school", "independent"),
     ("Other independent special school", "special"),
     ("Special post 16 institution", "special"),
     ("Further education", "post16"),
     ("Pupil referral unit", "alternative"),
-    ("academy CONVERTER", "academy"),
+    ("academy CONVERTER", "state"),
 ])
 def test_type_group_by_name(name, group):
     assert type_group_for(name) == group
 
 
+@pytest.mark.parametrize("value, key", [
+    ("state", "state"),
+    ("Special", "special"),
+    # The two state groups that preceded "state", kept so their links still work.
+    ("academy", "state"),
+    ("Council", "state"),
+    ("Community school", None),
+    ("", None),
+])
+def test_type_group_key_resolves_keys_and_old_keys(value, key):
+    assert type_group_key(value) == key
+
+
 @pytest.mark.parametrize("name", [
     "Higher education institutions", "Miscellaneous", "Unknown (9999)", "Academy", "", None, np.nan,
 ])