feat(search): school type groups and a faith filter

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

nextjs-app/lib/types.ts

@@ -484,6 +484,12 @@ export interface RankingsResponse {
   local_authority?: string;
 }
 
+/** A filter option whose URL value differs from what a parent reads. */
+export interface FilterOption {
+  value: string;
+  label: string;
+}
+
 export interface Filters {
   local_authorities: string[];
   school_types: string[];
@@ -491,6 +497,9 @@ export interface Filters {
   phases: string[];
   genders: string[];
   admissions_policies: string[];
+  /** Parent-facing school type groups; the URL's school_type takes their value. */
+  school_type_groups?: FilterOption[];
+  faiths?: FilterOption[];
 }
 
 export interface NationalAveragesYear {
@@ -567,6 +576,7 @@ export interface SchoolSearchParams {
   gender?: string;
   admissions_policy?: string;
   has_sixth_form?: string;
+  faith?: string;
 }
 
 export interface RankingsParams {