feat: fix search, poster serving, and add hover overlay UI for cards

- Fix search store exports to match component expectations (inputValue,
  bangumiList, onSearch) and transform data to SearchResult format
- Fix poster endpoint path check that incorrectly blocked all requests
- Add resolvePosterUrl utility to handle both external URLs and local paths
- Move tags into hover overlay on homepage cards and calendar cards
- Show title and tags on poster hover with dark semi-transparent styling
- Add downloader API, store, and page
- Update backend to async patterns and uv migration changes
- Remove .claude/settings.local.json from tracking

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

webui/src/utils/poster.ts

@@ -0,0 +1,5 @@
+export function resolvePosterUrl(link: string | null | undefined): string {
+  if (!link) return '';
+  if (link.startsWith('http://') || link.startsWith('https://')) return link;
+  return `/${link}`;
+}