It’s only theoretically non searchable, IIRC each submitted document has to be OCRed every time a search is ran on the documents, and this is enough of a legal fig leaf to qualify it as not a registry. A sizeable GPU farm would make this basically a moot point.

Oh I agree. It is very likely that the electronic checks are recorded and could be used as a non-official registry of gun owners. I removed my comment to that effect because it is speculation. But, electronic records are so easily recorded that I have little doubt that the electronic checks are in fact an illegal registry.

can the police not use a found weapon's serial number to determine its owner? how can they do that if there's no registry with that info?

Seven states have required gun registries. It is not illegal for a state to have a registry. It is illegal for the federal government to have a gun registry with exceptions for NFA controlled arms.

https://www.congress.gov/crs-product/IF12057