Are you allowed to transit VIE?
No new restrictions on transit.
If you have a transit with an overnight stay, are you allowed to leave the terminal
If you comply with all Schengen + Austria entry requirements, then this should not be a problem.
and go to an airport hotel (this is intra Schengen, so no border issues)?
If you are on a business trip (and can prove that), you can stay at the airport hotel.
If you are on a private/tourist trip, then it's not allowed anymore. That is the biggest change due to the lockdown.
I find nothing in the info released so far, nor do I find an official text of the regulation - has it been written at all?
What still do you want to know?
Most of your question had been answered already.
Also I am curious - are Austrians permitted to travel to other countries during the lockdown for non-essential purposes?
What other countries will do, we cannot predict that. Austrian citizens are allowed to leave Austria for any reason.
After all, traveling away is the best possible contribution one can make to lowering the Covid-19 incidence rate.
That is not true. Travel spreads the virus.