fix(filters): forward gender, admissions_policy, has_sixth_form to API

These params were present in the URL but never passed to fetchSchools on
the server side, so the backend never applied the filters. Also include
them in hasSearchParams so filter-only searches trigger a fetch.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

nextjs-app/app/page.tsx

@@ -16,6 +16,9 @@ interface HomePageProps {
     postcode?: string;
     radius?: string;
     sort?: string;
+    gender?: string;
+    admissions_policy?: string;
+    has_sixth_form?: string;
   }>;
 }
 
@@ -41,7 +44,10 @@ export default async function HomePage({ searchParams }: HomePageProps) {
     params.local_authority ||
     params.school_type ||
     params.phase ||
-    params.postcode
+    params.postcode ||
+    params.gender ||
+    params.admissions_policy ||
+    params.has_sixth_form
   );
 
   // Fetch data on server with error handling
@@ -60,6 +66,9 @@ export default async function HomePage({ searchParams }: HomePageProps) {
         radius,
         page,
         page_size: 50,
+        gender: params.gender,
+        admissions_policy: params.admissions_policy,
+        has_sixth_form: params.has_sixth_form,
       });
     } else {
       // Empty state by default