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/Home.vue

@@ -54,7 +54,7 @@
           v-for="song in store.dailySongs.slice(0, 12)"
           :key="song.id"
           class="daily-card hover-scale"
-          @click="store.play(song.name, song.platform)"
+          @click="store.playById(song.id, song.platform)"
         >
           <CoverArt :url="song.coverUrl" :size="120" :radius="10" :show-shadow="true" />
           <div class="daily-name">{{ song.name }}</div>