I've been struggling with an issue where the centre of the phone doesn't pick up the pen when using it. Done all the troubleshooting and sent the phone in through samsung support but returned unrepaired.
I'm seeing I'm not the only one with this issue with the fold 4, no phone case,error continues on safe mode, without a case and even after factory reset.
You can try diagnostic within Samsung member app and run S Pen check to test touchscreen and see if your pen colours the squares blue in the centre of screen.
If it does then may be issue with s pen see its settings and if it doesn't then you have issue with screen and raise with Samsung