feat: play-by-id and play-playlist endpoints, fix lyrics sync timing

- New endpoints: play-by-id, add-by-id, play-playlist (load all songs at once)
- Playlist 'Play All' now uses server-side bulk load (no N sequential searches)
- Search/Home/Playlist views use playById instead of search-by-name
- Fixed updateBotStatus timing: capture prev state before mutation
- Early return on song change prevents stale pause/resume logic

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

web/src/views/Search.vue

@@ -27,8 +27,8 @@
         :song="song"
         :index="i + 1"
         :active="store.currentSong?.id === song.id"
-        @play="store.play(song.name, song.platform)"
-        @add="store.addToQueue(song.name, song.platform)"
+        @play="store.playById(song.id, song.platform)"
+        @add="store.addToQueueById(song.id, song.platform)"
       />
     </div>