Fix correctness bugs found by code review

- matrix: drop cryptohelper LoginAs so device.json creds aren't
  invalidated on every restart by Init's re-login
- matrix: thread ctx through PostThreadedReply; bot dispatcher derives
  per-command ctx from app lifecycle so SIGTERM cancels in-flight work
- matrix: isTokenValid verifies /whoami user_id matches configured one
- matrix: loadDevice distinguishes missing file from corrupt parse;
  refuse to silently overwrite a corrupt device.json
- matrix: Start checks Syncer type assertion and returns error
- arr: parseLookup skips empty-title items and extracts existing id
- bot: skip Add when Result.Exists; reply "already in library"

main.go

@@ -43,13 +43,17 @@ func main() {
 		os.Exit(1)
 	}
 
-	dispatcher := bot.New(cfg.Matrix.CommandPrefix, services, mx)
-	mx.SetMessageHandler(dispatcher.Handle)
-
 	ctx, cancel := context.WithCancel(context.Background())
 	defer cancel()
 
-	mx.Start(ctx)
+	dispatcher := bot.New(ctx, cfg.Matrix.CommandPrefix, services, mx)
+	mx.SetMessageHandler(dispatcher.Handle)
+
+	if err := mx.Start(ctx); err != nil {
+		slog.Error("matrix start failed", "err", err)
+		mx.Stop()
+		os.Exit(1)
+	}
 	slog.Info("bellhop started", "allowed_rooms", len(cfg.Matrix.AllowedRooms))
 
 	sig := make(chan os.Signal, 1)