I don't see "leaving Austria" listed as a legitimate reason to leave your home under the new regulations, so how are you going to get to the airport?
This is allowed. This was also no problem during the last lockdown.
So basically, if a transit passenger is on a business trip, he gets to sleep in an airport hotel. If he is on a private trip, he is sleeping on a bench in the terminal, correct?
Yes, this is the case.