I am a US citizen with permanent residence in Sweden flying from the US to Sweden next week via Frankfurt. Do I need a negative COVID test to make this trip? The Swedish migration website says I do not (https://polisen.se/en/the-swedish-po...d-from-sweden/), and the Frankfurt website says that transit passengers with onward travel to a Schengen country might not need to present a test (cf. https://www.lufthansa.com/us/en/entry-into-germany).

On the other hand, the US embassy website says I do need a test (https://de.usembassy.gov/covid-19-information/).

I'm wondering if anyone with experience can tell me which is right? I'm more inclined to believe I do not need a test, but don't want to show up in Germany without one if they require it.