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

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

nextjs-app/app/(frontend)/page.tsx

@@ -25,6 +25,7 @@ interface HomePageProps {
     gender?: string;
     admissions_policy?: string;
     has_sixth_form?: string;
+    faith?: string;
   }>;
 }
 
@@ -84,7 +85,8 @@ export default async function HomePage({ searchParams }: HomePageProps) {
     params.postcode ||
     params.gender ||
     params.admissions_policy ||
-    params.has_sixth_form
+    params.has_sixth_form ||
+    params.faith
   );
 
   // Failures propagate to the retryable error boundary.
@@ -105,6 +107,7 @@ export default async function HomePage({ searchParams }: HomePageProps) {
       gender: params.gender,
       admissions_policy: params.admissions_policy,
       has_sixth_form: params.has_sixth_form,
+      faith: params.faith,
     });
   } else {
     // Empty state by default