fix(search): start postcode searches at half a mile

New postcode searches, the near-me button and URLs without a radius now
use 0.5 miles. A postcode URL with no radius used to show "1 mile" in the
Distance control while the API applied its own 5-mile default; the page
and the map fetch now send the same default the control displays.

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

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

@@ -0,0 +1,41 @@
+import { render, screen, waitFor } from '@testing-library/react';
+import userEvent from '@testing-library/user-event';
+import { FilterBar } from '@/components/FilterBar';
+
+const push = jest.fn();
+let searchParams = new URLSearchParams();
+jest.mock('next/navigation', () => ({
+  useRouter: () => ({ push, replace: jest.fn(), prefetch: jest.fn() }),
+  usePathname: () => '/',
+  useSearchParams: () => searchParams,
+}));
+
+const FILTERS = {
+  local_authorities: [], school_types: [], years: [], phases: [],
+  genders: [], admissions_policies: [],
+};
+
+beforeEach(() => {
+  push.mockClear();
+  searchParams = new URLSearchParams();
+});
+
+describe('FilterBar default distance', () => {
+  it('searches a new postcode within half a mile', async () => {
+    render(<FilterBar filters={FILTERS} />);
+    await userEvent.type(screen.getByPlaceholderText(/School name or postcode/i), 'SW19 6AR{Enter}');
+    await waitFor(() => expect(push).toHaveBeenCalledWith(expect.stringContaining('radius=0.5')));
+  });
+
+  it('shows half a mile when the URL carries a postcode but no radius', () => {
+    searchParams = new URLSearchParams('postcode=SW196AR');
+    render(<FilterBar filters={FILTERS} />);
+    expect(screen.getByRole('combobox', { name: 'Distance' })).toHaveValue('0.5');
+  });
+
+  it('keeps a distance the user already chose', async () => {
+    searchParams = new URLSearchParams('postcode=SW196AR&radius=3');
+    render(<FilterBar filters={FILTERS} />);
+    expect(screen.getByRole('combobox', { name: 'Distance' })).toHaveValue('3');
+  });
+});