Rebuilt the Library page to reuse the music library's exact look — no
reinvention, just new data:
- Same classes: .library-container, .library-artist-card grid, .alphabet-
selector, .library-search-input, loading/empty states. Movies/Shows tab pill
is the only video-specific bit.
- Real posters via a server-side proxy: GET /api/video/poster/<kind>/<id>
streams the Plex/Jellyfin artwork (token stays server-side); cards fall back
to an emoji on miss. list_movies/list_shows now expose has_poster (no raw
server paths leaked).
- Client-side search + A-Z letter filter (article-aware) over the loaded set;
cards are divs (not clickable yet, per request). Scan button in the header
reuses the shared scan controller and reloads on done.
110 tests green.
