I don't think self-tests would qualify for Americans returning to the US.

I am going to be facing the same issue in a few weeks, around the middle of August, when I will be departing from Verona.

In France, many pharmacies offer antigen tests for a fee but in Spain they only sell self-test kits.

So it would be nice if you could walk into any Italian pharmacy and get an antigen test, not a self-test kit.