feat(search): filter on phones through one sheet

On phones the results toolbar's filters were a sideways-scrolling row
led by "More filters", so phase showed only in part and school type not
at all, and the panel "More filters" opened held neither of them.

Phones now get a single Filters button beside the folded search summary,
counting every applied filter. It opens a bottom sheet with every filter:
distance as five segments, then phase, school type, local authority and
the secondary-only filters. Changes apply at once, as on desktop, so the
footer's "Show N schools" only closes the sheet. Applied filters show as
removable chips on a second line, which appears only when something is
applied. Desktop and tablet are unchanged.

Modal gains dialog semantics, a pinned footer and focus handling, and
moves above the pinned toolbar, the floating List/Map button and the
comparison toast, which its old z-index sat beneath.

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

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

@@ -105,11 +105,21 @@ describe('the toolbar filters', () => {
   });
 });
 
-describe('the phone filter row', () => {
+describe('the phone chips line', () => {
   it('drops its "more this way" fade when nothing is left to scroll', () => {
+    params = new URLSearchParams('postcode=SW196AR&radius=1&phase=primary');
     render(<FilterBar filters={filters} />);
-    // jsdom lays nothing out, so the row reads as not overflowing at all.
-    expect(screen.getByRole('group', { name: 'Filters' }).className).toMatch(/controlsAtEnd/);
+    // jsdom lays nothing out, so the line reads as not overflowing at all.
+    const line = screen.getByRole('group', { name: 'Applied filters' }).parentElement!;
+    expect(line.className).toMatch(/controlsAtEnd/);
+  });
+});
+
+describe('the phone filter sheet', () => {
+  it('offers the results total', () => {
+    render(<HomeView initialSchools={results()} filters={filters} />);
+    fireEvent.click(screen.getByRole('button', { name: 'Filters' }));
+    expect(screen.getByRole('button', { name: 'Show 1 school' })).toBeInTheDocument();
   });
 });