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/components/Modal.module.css

@@ -5,7 +5,9 @@
   display: flex;
   align-items: center;
   justify-content: center;
-  z-index: 1000;
+  /* Above the pinned results toolbar (1001), the floating List/Map button
+     (1002) and the comparison toast (2000): a modal covers the page. */
+  z-index: 2100;
   padding: 1rem;
   animation: fadeIn 0.2s ease;
 }
@@ -31,6 +33,10 @@
   border: 1px solid var(--border);
 }
 
+.modal:focus {
+  outline: none;
+}
+
 @keyframes slideIn {
   from {
     transform: translateY(-20px);
@@ -96,6 +102,14 @@
   flex: 1;
 }
 
+/* Clears the iPhone home indicator when the modal is a bottom sheet. */
+.footer {
+  flex-shrink: 0;
+  padding: 0.75rem 1rem calc(0.75rem + env(safe-area-inset-bottom, 0px));
+  border-top: 1px solid var(--border);
+  background: var(--bg-card);
+}
+
 /* Scrollbar styles */
 .content::-webkit-scrollbar {
   width: 8px;