A foreigner in Germany is required to be able to produce a passport when an authority asks for it. https://dejure.org/gesetze/AufenthG/48.html

In practical life, if you do not carry your passport with you and you are stopped, your plans for the day are on hold until the authority has seen your passport in original. Mostly they will accompany you to your hotel or whereever you may have safely stored your passport.

US passport cards are not ID allowed by Germany, but EU citizens can use their national ID cards. Driving Licences issued anywhere are not ID in Germany, they are just a licence to drive.