Traveling to Italy with Dual US/DE Citizenship [duplicate]

Your assumptions about the EU are wrong. The US definitely requires airlines to give them Advance Passenger Information and technically makes it mandatory for citizens to use their US passport but most other countries don't and all this is far less systematic than you seem to imagine.

Specifically, there are many advantages but certainly no obligation to disclose your EU citizenship when entering the EU. Individual countries might theoretically have a requirement like that for their own citizens but you're not an Italian citizen so it wouldn't concern you. And if you choose to show your US passport at a kiosk, there is nothing preventing you from using your German passport at the destination anyway.

The problem with doing something like that in the other direction (flying to the US) is that almost everybody requires prior authorisation (a visa or ESTA). So if you would use your German passport to fly to the US, it would be flagged because you have no ESTA (and could not get one without lying as US citizens are not supposed to and the form asks you to disclose any other citizenship IIRC). But that's not an issue in this case, as US citizens do not require a visa or authorisation to enter the Schengen area.

You should leave the US on your US passport and enter the EU on your German passport. Vice versa on return..