I haven’t undergone an on-site NICS check for 15-20 years. Ever since I’ve had my GFL/WCL here in Georgia. That card lets me bypass the NICS any time I buy a weapon. The license is good for 5 years. Three/Four NICS checks for the licenses - how many guns do you suppose I bought during that time?
There is NO REASON why the serial number of a weapon should be on the Background check. You voluntarily give the government the information they need when they want to confiscate your weapons.