score:4
No, there is definitely no stamping between Austria and Germany in one direction or the other, no matter how you travel.
Usually, I would also say that you are unlikely to even talk to a police officer but, increasingly, there are “random” checks, especially on trains and other land borders but perhaps more frequently in the other direction (Austria to Germany). It's difficult to quantify that exactly but many anecdotal reports also suggest that border police in many European countries take a special interests in people who look “non-European” so if you “look Indian”, you might have to face that, sadly.
By plane, I would still expect no control whatsoever. But if there is one, showing your passport and Schengen visa/German entry stamp will be enough and your documents should not be stamped again in either Vienna or Klagenfurt.