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>

docs/superpowers/specs/2026-10-02-school-type-groups-and-faith-filter-design.md

@@ -1,14 +1,24 @@
 # School Type Groups and a Faith Filter — Design
 
 **Date:** 2026-10-02
-**Status:** approved in conversation, awaiting spec review
+**Status:** shipped in PR #170; revised 2026-10-02 (one state group)
 **Scope:** search filters (`/` results toolbar and phone filter sheet), `/api/schools`, `/api/filters`
 
 ## Goal
 
-Replace the School type filter's 34 GIAS establishment types with six groups a
+Replace the School type filter's 34 GIAS establishment types with five groups a
 parent recognises, and add a Faith filter.
 
+> **Revision, 2026-10-02.** PR #170 shipped six groups, with state schools
+> split into "academy or free school" and "council-run". They are now one,
+> "State school (free)". The split was two near-halves of the same pool, so it
+> rarely narrowed anything, and it did not follow the difference a parent feels
+> most, admissions: voluntary aided and foundation schools set their own
+> admissions, as academies do, while community and voluntary controlled
+> schools have theirs set by the council. Faith, which voluntary aided mostly
+> meant, has its own filter. The old keys `academy` and `council` resolve to
+> `state`, so their links keep working.
+
 Since PR #169 the School type select offers the full GIAS list rather than the
 types in the results. That fixed the trap where choosing a type left only that
 type on offer, but it exposed the list itself: "Academy converter", "Academy
@@ -44,8 +54,7 @@ Order is the order shown. Codes are GIAS `TypeOfEstablishment` codes
 
 | Key | Label | GIAS codes | Schools |
 |---|---|---|---|
-| `academy` | State school: academy or free school | 28 Academy sponsor led, 34 Academy converter, 35 Free schools, 40 University technical college, 41 Studio schools, 6 City technology college | 11,186 |
-| `council` | State school: council-run | 1 Community school, 2 Voluntary aided school, 3 Voluntary controlled school, 5 Foundation school, 15 Local authority nursery school | 9,316 |
+| `state` | State school (free) | 28 Academy sponsor led, 34 Academy converter, 35 Free schools, 40 University technical college, 41 Studio schools, 6 City technology college, 1 Community school, 2 Voluntary aided school, 3 Voluntary controlled school, 5 Foundation school, 15 Local authority nursery school | 20,502 |
 | `independent` | Independent (fee-paying) | 11 Other independent school | 1,585 |
 | `special` | Special school (SEND) | 7 Community special, 12 Foundation special, 44 Academy special converter, 33 Academy special sponsor led, 36 Free schools special, 8 Non-maintained special, 10 Other independent special, 32 Special post 16 institution | 2,227 |
 | `post16` | Sixth form or college | 18 Further education, 31 Sixth form centres, 45 Academy 16-19 converter, 46 Academy 16 to 19 sponsor led, 39 Free schools 16 to 19 | 302 |
@@ -64,9 +73,11 @@ department. 238 schools.
 - **Independent special schools are Special, not Independent.** They are
   usually funded by the local authority through a child's EHCP; to a parent
   they are SEND provision, not private school.
-- **UTCs, studio schools and city technology colleges are academies.** They are
-  legally academies, they are few (66 together), and a family considering one
-  searches for it by name.
+- **UTCs, studio schools and city technology colleges are state schools.** They
+  are legally academies, they are few (66 together), and a family considering
+  one searches for it by name.
+- **Academies and council-run schools are one group.** See the revision note
+  under Goal.
 - **Special post 16 institutions are Special, not Sixth form or college.** The
   defining fact for a parent is the SEND provision.
 - **Alternative provision is last.** Parents do not apply to it; the local