When I got the PCR COVID test administered when I had a suspected case, I was required to fill out a form stating my name, DOB, email, phone, physical address, full social security number, and student ID (I'm a college student). Since these are all attributes bound to identity, I'm sure it's not too difficult to make a database of test results.
...Just from the thought of it, forcing other countries to store your private info would be a terrible idea considering they probably could care less about it being stolen.
But, you are entirely missing the point. The U.S. cannot mandate that other countries maintain a database with U.S. citizens personal info, even if your idea didn't have massive gaping holes in it regarding security. It is simply impossible.
