Current the actual rules no Test needed The EU Certificate with 3 vaccinations are enough.

check reopeneurope.com

From what I know (but DO double check) for DE-AT you are Ok with the QR code with the booster. In fact I do not recall any countries where a new test has to be taken for use trains when you have the booster. SOME countries (I think ITaly for now and maybe Switzerland) want to see a test before entry-not specific for train riding. But to visit some specific places in DE you may have to take a cheap antigentest again. varies per region.

If you also travel by train to Wien, maybe you also pass Switzerland?

It may also depend if you have visited other countries the last 14 days.

@mcadv 

Test in Switzerland not needed if boosterd (3rd Vaccination)
Italy still always a test needed (doesn´t matter if 2 or 3 Vaccinations shots)

You don’t need an extra test to enter Italy. They changed it. But vaccinations (the first 2 doses) are valid only 6 months* (like in Austria and not 9 months, like in the rest of the EU) and recovery max. 4 months.

Booster without expire date. 

You need a vaccination or recovery (2G rule or “Super Green Pass”) to use trains and public transportation in Italy. 

Don’t forget to do the Passanger Location Form before entering Italy. 

*For People from countries whit the 9 months rule (Vaccination between 6-9 months), can enter Italy and use the trains there but needs also an antigenic test (max. 48h) or PCR (max. 72h).