fix(search): desktop Clear all keeps the search

The desktop toolbar's Clear went to the bare home URL, dropping the
search along with the filters, so it landed on the home page instead of
the unfiltered results. It now clears every filter and keeps the search,
postcode and distance, as the phone's Clear all already did. It is
offered only once a filter is applied, since with only a search there is
nothing for it to clear, and is labelled Clear all to match the phone.

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

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

@@ -1,4 +1,4 @@
-import { act, fireEvent, render, screen } from '@testing-library/react';
+import { act, fireEvent, render, screen, within } from '@testing-library/react';
 import { HomeView } from '@/components/HomeView';
 import { FilterBar } from '@/components/FilterBar';
 import { fetchSchools } from '@/lib/api';
@@ -175,3 +175,24 @@ describe('the results list', () => {
     expect(screen.queryByText('Search: southmead')).not.toBeInTheDocument();
   });
 });
+
+describe('the desktop Clear all', () => {
+  const row = () => screen.getByRole('group', { name: 'Filters' });
+
+  it('removes the filters and keeps the search, rather than going home', () => {
+    params = new URLSearchParams('postcode=SW196AR&radius=3&phase=primary&school_type=council&local_authority=Wandsworth');
+    render(<FilterBar filters={filters} />);
+    fireEvent.click(within(row()).getByRole('button', { name: 'Clear all' }));
+    const pushed = push.mock.calls.at(-1)![0] as string;
+    const next = new URLSearchParams(pushed.split('?')[1]);
+    expect(next.get('postcode')).toBe('SW196AR');
+    expect(next.get('radius')).toBe('3');
+    for (const key of ['phase', 'school_type', 'local_authority']) expect(next.get(key)).toBeNull();
+  });
+
+  it('is not offered when only a search is applied', () => {
+    params = new URLSearchParams('search=southmead');
+    render(<FilterBar filters={filters} />);
+    expect(within(row()).queryByRole('button', { name: /^Clear/ })).not.toBeInTheDocument();
+  });
+});