Hello mzeb,
Thank you for using Apple Support Communities. Sounds like you're noticing some delay issues when using your gaming controller with your Mac. If so, we'd like to help out in any way we can. There's a few basic steps you can try to help isolate this issue. Follow the steps below:
1.) Try a simple restart of your Mac. This usually helps refresh things: Shut down or restart your Mac - Apple Support
2.) Unpair and re-pair your Bluetooth accessory.
3.) Make sure that all updates have been installed for your Mac. Updates usually do include various fixes: Update macOS on Mac - Apple Support
4.) If you're already fully updated, test this issue in safe mode. This step can help isolate possible software related issues: How to use safe mode on your Mac - Apple Support
Apple silicon
1.) Shut down your Mac.
2.) Turn on your Mac and continue to press and hold the power button until you see the startup options window.
3.) Select your startup disk, then press and hold the Shift key while clicking “Continue in Safe Mode.”
4.) Log in to your Mac. You might be asked to log in again.
Depending on your results, follow the steps under “If the issue continues in safe mode” or “If the issue doesn't continue in safe mode”.
We hope this helps you. Thank you for using Apple Support Communities. Take care.