Add full-text search

- Index notes in a separate, rebuildable SQLite database (index.db) using FTS5 trigram,
  synced from watcher snapshots so external edits are picked up; terms under 3 characters
  fall back to LIKE
- GET /api/v1/search?q= returns matching notes with the first matching line and a snippet;
  path matches rank first
- Sidebar search panel (Ctrl+Shift+F) with highlighted terms and keyboard navigation;
  opening a result jumps to and selects the match
- Restore scroll position on tab switch with scroll snapshots; restoring scrollTop drifted
  by a few lines after line heights were re-estimated

web/src/app/Icon.vue

@@ -13,6 +13,7 @@ const paths = {
   logout: 'M9 21H5a2 2 0 0 1-2-2V5a2 2 0 0 1 2-2h4M16 17l5-5-5-5M21 12H9',
   restore: 'M3 12a9 9 0 1 0 3-6.7L3 8M3 3v5h5',
   edit: 'M12 20h9M16.5 3.5a2.1 2.1 0 0 1 3 3L7 19l-4 1 1-4z',
+  search: 'M11 18a7 7 0 1 0 0-14 7 7 0 0 0 0 14zM21 21l-4.35-4.35',
 }
 defineProps<{ name: keyof typeof paths; size?: number }>()
 </script>