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>

src/web/server.ts

@@ -46,7 +46,10 @@ export function createWebServer(options: WebServerOptions): WebServer {
     "/api/music",
     createMusicRouter(options.neteaseProvider, options.qqProvider, logger)
   );
-  app.use("/api/player", createPlayerRouter(options.botManager, logger, options.database));
+  app.use("/api/player", createPlayerRouter(
+    options.botManager, logger, options.database,
+    options.neteaseProvider, options.qqProvider,
+  ));
   app.use(
     "/api/auth",
     createAuthRouter(options.neteaseProvider, options.qqProvider, logger, options.cookieStore)