One thing to keep in mind is that the information on the 4473 that links a gun to you by serial # is NOT given to the federal govt to put in a database, they have to go LOOK for it.
Your state may have their own rules but that's your state. Your state may hand over the information to the Fed, I have no idea, but I would expect that the Fed would have to request it.
No instant background check over the phone by an FFL that I have been involved with has EVER given the gun serial#. Your/my personal info (DOB, address etc) and either "handgun or long gun". Only that, never the gun serial #.
SO, the Fed knows you bought a gun, and they know if its a handgun, or not. And that's it. For further info, they have to go LOOK at the dealers PHYSICAL records. They have to go the shop and look at the papers. They can, and do this, easily enough, if they have a reason. But they don't get to just push a button and get a list of what you bought by serial #.
However, once they HAVE that list, I think they would save it, somewhere they can get it with a push of a button, or mouseclick.
I find the information about how the Fed is ruling on what tools you can use to build your own gun to be ....entertaining, and you know the only reason they even exist now is because of idiots baiting the Fed with the whole "ghost gun" foolishness.
Foolishness, because we were fine, and largely left alone by the ATF if we were only making firearms for personal use. The only real concern was how many one could make before the Fed felt you needed a manufacturer's license. The Fed didn't care WHO'S tools you used, only if you were doing it for sale or not.
Of course, this was also in the days when you had to have machine tool operating skills, or a LOT of determination and patience with a file.
Emotional children, discovering the tech that let them make (SOME) gun parts via a 3d printer, dancing and capering about (on the internet, particularly) with tongues stuck out, thumbs in their ears wiggling their fingers at the ATF and chanting "neener neener, we can make ghost guns!" was a rather STUPID thing to do, in my opinion. THANKS SO MUCH, fellahs.
If you're doing it for the joy of building your own gun, fine. Wonderful, even.
If you're doing it so its not registered to you, (check your LOCAL laws carefully, as well!) it seems to me that it would be simpler, and maybe cheaper to just buy a used gun from a private seller. (where legal)
There are still many places in the country where its not only still legal, but encouraged. Sadly not as many as there used to be...