A few years ago, I owned both a Colt AR-15 and a Heckler and Koch HK-91. I thought it was interesting that the serial number on the HK-91 (as is the case in most rifles) was on the upper receiver, but the AR-15 was on the lower. I wondered how Stoner and Armalite decided, or were instructed by the government, to stamp the serial number. But even if the government regulations are vague as to the definition of “receiver”, I bet the courts would eventually decide that whatever rifle part has the serial number stamped on it is the part regulated by law. If you purchase or ship a serial-numbered handgun frame or a rifle receiver, you have to consider the applicable laws. All other parts are just “parts”, not subject to regulations.
I had a HK-91 some 30 years ago. IIRC, it did not separate in to upper and lower receiver, so where the S/N was stamped would not matter.