What steps can I take to troubleshoot the "r6s error at hooking api" error if I suspect a third-party application is the cause?

The best approach is to disable all non-essential third-party applications, especially overlays and monitoring tools. Start by closing one application at a time and relaunching the game to see if the error persists. This process of elimination will help identify the specific program causing the conflict. After identifying the problem application, consider updating it or uninstalling it if it's not critical.