docs(spec): describe the API filters as they are built

The /api/schools section still described filtering on stored
school_type_group and faith_groups columns, which the architecture
correction had already dropped: the filters look up the name columns at
request time. Also trims a trailing blank line from two test files.

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

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

@@ -131,13 +131,20 @@ names. The names come from the same dictionaries, so the lookup is exact.
 
 ### `/api/schools`
 
-- `school_type`: if the value is a type group key, filter on
-  `school_type_group`. Otherwise filter on the raw label exactly as today, so
-  an old `?school_type=Community+school` link keeps working.
-- `faith` (new, optional, `max_length=40`, sanitised like the others): filter to
-  rows whose `faith_groups` contains the key. An unknown key returns no
-  schools rather than being ignored, so a typo does not silently show
-  everything.
+Both filters work on the name columns at request time. `_names_in_group`
+collects the distinct `school_type` or `religious_denomination` names the
+group accepts, once per distinct name rather than per row, and the rows are
+kept with `isin`. No group column is stored.
+
+- `school_type`: if the value is a type group key (any case), keep the rows
+  whose `school_type` name `type_group_for` puts in that group. Otherwise
+  filter on the raw label exactly as today, so an old
+  `?school_type=Community+school` link keeps working.
+- `faith` (new, optional, `max_length=40`, sanitised like the others): keep the
+  rows whose `religious_denomination` name `faith_groups_for` puts in that
+  faith (any case); for `none`, rows with a missing name too. An unknown key
+  returns no schools rather than being ignored, so a typo does not silently
+  show everything.
 
 ### `/api/filters`
 

nextjs-app/__tests__/components/FilterBarTypeFaith.test.tsx

@@ -135,4 +135,3 @@ describe('a URL value the options do not spell the same way', () => {
     expect(screen.getByRole('combobox', { name: 'Faith' })).toHaveValue('roman_catholic');
   });
 });
-

nextjs-app/__tests__/components/ResultsToolbar.test.tsx

@@ -176,4 +176,3 @@ describe('the results list filter chips', () => {
     expect(chips).not.toHaveTextContent(/\bcouncil\b(?!-run)/);
   });
 });
-