The FDA has approved 13 test kits for at-home use with a self-collected sample, according to https://www.fda.gov/medical-devices/coronavirus-covid-19-and...

Germany has approved a much larger number of test kits for use, per https://antigentest.bfarm.de/ords/f?p=110:100:4793921863454:::::. It was >50 as of August 2021 according to https://marginalrevolution.com/marginalrevolution/2021/08/te..., including from American companies that the FDA has not approved.

I suspect that the supply-restriction effects of the approval situation go a long way toward explaining the pricing differences...