The rules in Austria will radically change on the 19th of May.
For the immigration side of the question, as a resident of Germany you may freely enter Austria and return to Germany.
At the moment there are about 32 daily train connections between the 2 cities.
Covid-19 conditions when returning to Germany will be based on whether you are fully vaccinated (or recovered) or not.
A test is presenty not required for those who are fully vaccinated (or recovered).
The entry rules for Austria (starting on the 19th) have not yet been finalized, but it has been announced that vaccinated (or recovered) do not require a test.
Note: the Austrian text does not use the word fully, so this is a bit ambiguous.
For visiting restaurants, hotels, culture and sport events, no test will be required for persons 22 days after they have recieved the 1st vaccination or have recovered.
This law has been finalized and comes into effect on the 19th of May.