First close all the Unreal Engine processes, wait a bit, then go into task manager and kill any remaining Unreal Editor processes if any exist. If there were any processes, try starting unreal the normal way and see if the issue persist, if not , go to the next step.
Is your account an admin? Do you have the proper write rights set up for the directory shown in the unreal error? Could be you need to set write permissions for your account for that directory, it’s the panel on the screenshot I sent earlier except permissions should show “Allow”.
My guess is that you accidentally modified the folder rights at some point of some game folder which now refuses to cooperate with Unreal. Or, you are using a different OS profile which has rights to one project but not the other.