feat(mobile): search box in the Select Case picker (#488)

The phone case picker had no way to narrow a long case list, so finding
one meant scrolling a sheet that showed about six rows at a time.

- A search field filters rows by name (every typed word must match, any
  order, case-insensitive), with a "No matching cases" state. Enter picks
  the case when exactly one row is left; Escape clears, then closes.
- The field is not auto-focused, so opening the picker does not raise the
  keyboard. The list holds its unfiltered height while searching so the
  sheet does not jump, and the input is 16px so iOS Safari does not zoom.
- Layout: the sheet padded the home-indicator inset on top of the footer
  already doing so, leaving a dead band under Create New Case; the sheet
  now grows to 80dvh and the list fills it instead of a separate 50vh cap.
- Opening scrolls the list (its own box, not scrollIntoView) to the
  currently selected case.

Co-authored-by: Codeman maintainer <noreply@anthropic.com>

src/web/public/session-ui.js

@@ -4589,6 +4589,7 @@ Object.assign(CodemanApp.prototype, {
       const isSelected = c.name === currentCase;
       html += `
         <button class="mobile-case-item ${isSelected ? 'selected' : ''}"
+                data-search="${escapeHtml(`${c.label} ${c.name}`.toLowerCase())}"
                 onclick="app.selectMobileCase(${escapeHtml(JSON.stringify(c.name))})">
           <span class="mobile-case-item-icon">
             <svg width="18" height="18" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
@@ -4611,7 +4612,61 @@ Object.assign(CodemanApp.prototype, {
     }
 
     listContainer.innerHTML = html;
+    // Every open starts unfiltered. The search box is not focused on purpose:
+    // that would raise the phone keyboard over a list most opens just tap.
+    const search = document.getElementById('mobileCaseSearch');
+    if (search) search.value = '';
+    listContainer.parentElement.style.minHeight = '';
+    this.filterMobileCases();
     modal.classList.add('active');
+    // Bring the current case into view when the list is longer than the sheet.
+    // Scroll the list's own box, never scrollIntoView(), which can also scroll
+    // the document under the fixed header.
+    const body = listContainer.parentElement;
+    const selected = listContainer.querySelector('.mobile-case-item.selected');
+    if (body && selected) {
+      const top = selected.offsetTop - body.offsetTop;
+      if (top + selected.offsetHeight > body.scrollTop + body.clientHeight) {
+        body.scrollTop = top - (body.clientHeight - selected.offsetHeight) / 2;
+      }
+    }
+  },
+
+  /** Hide case rows whose name does not contain every word typed in the search box. */
+  filterMobileCases() {
+    const search = document.getElementById('mobileCaseSearch');
+    const words = (search?.value || '').toLowerCase().split(/\s+/).filter(Boolean);
+    // Hold the list at its unfiltered height while searching, so the sheet (and
+    // the input under the thumb) does not jump as rows disappear.
+    const body = document.querySelector('.mobile-case-picker-body');
+    if (body && words.length && !body.style.minHeight) body.style.minHeight = `${body.offsetHeight}px`;
+    let shown = 0;
+    for (const item of document.querySelectorAll('#mobileCaseList .mobile-case-item')) {
+      const hay = item.dataset.search || '';
+      const match = words.every((w) => hay.includes(w));
+      item.hidden = !match;
+      if (match) shown++;
+    }
+    const empty = document.getElementById('mobileCaseEmpty');
+    if (empty) empty.hidden = shown > 0;
+  },
+
+  /** Enter picks the case when the search narrows the list to exactly one; Escape clears, then closes. */
+  onMobileCaseSearchKey(event) {
+    if (event.key === 'Enter') {
+      event.preventDefault();
+      const visible = [...document.querySelectorAll('#mobileCaseList .mobile-case-item:not([hidden])')];
+      if (visible.length === 1) visible[0].click();
+    } else if (event.key === 'Escape') {
+      event.preventDefault();
+      event.stopPropagation();
+      if (event.target.value) {
+        event.target.value = '';
+        this.filterMobileCases();
+      } else {
+        this.closeMobileCasePicker();
+      }
+    }
   },
 
   closeMobileCasePicker() {