Just checked this with the Austrian border policy section.
In case of doubt, you may be asked for proof of residence in Germany (not because residence in Germany is required, but to support your claim that you haven’t been to a high-risk country).
This can be a Meldebescheinigung (if having lived in Germany for less than 5 years) or a Bescheinigung des Daueraufenthalts (if having lived in Germany for 5 years or more)
I’ve traveled by car from Italy to Austria recently and here’s how their border control looks like:
Quite frankly I’m not sure how you would even be able to produce such documentation given that EU citizens don’t get stamped at the border. So it’s effectively an honor system.
Credit:stackoverflow.com‘