Isn’t this just back door gun registration?
Ex: if you buy 9mm and they don’t have a record of you owning a 9mm pistol then you must have one.
I seriously doubt they are ever going to purge records, even for the law abiding.
We already have firearms registration.
Not that it would affect what gun-grabbers might do, but many firearms are "multi-caliber". You can change upper assemblies & mags on most ARs; you can swap cylinders with some revolvers; and you fit different slide/barrel/magazine combinations to many auto pistols. A law abiding citizen might therefore purchase ammunition in a half-dozen (or more) different calibers for a single firearm...