No, the OP is fully vaccinated. No test required for travel to or through Germany when originating from the US.

The real issue isn't testing. It is if the new EU agreement to re-open to fully vaccinated travellers (from most countries, with possible exceptions for worrisome variants) will be implemented prior to OP's travel. As I wrote above, I think it will become law in time.

EDIT: Same for Croatia. You won't need a test if fully vaccinated using an approved vaccine such as Pfizer or Moderna.