This is incorrect.

Austria is NOT a member of NATO, and is politically neutral per its constitution from 1955 at the end of Allied post-WWII occupation. So unlike every other member of Western/Central Europe, there are zero non-Austrian troops and/or bases in Austria.

Because of its neutrality, throughout the cold war Austria was seen as "neutral ground" for spies on both sides of the iron curtain. Also because of its neutrality, there are a huge number of international groups headquartered in Vienna e.g. IAEA, OSCE.

All that above are small potatoes compared to the real reason - energy. Austria gets most of its gas from Russia. Oil not so much, but gas is 80%+. So when the idea for a Russian gas boycott was floated in the EU, Austria said, "Nein, danke."

That is the consumer side. The business-side is just as important. OPEC is headquartered in Vienna. OMV, the quasi-state Austrian energy giant, has business all over the world. OMV has an enormous number of joint ventures up and down the energy supply chain. A lot of those joint ventures are in Russia or in Russian allied countries. Making them Austrian allied countries. OMV also has been doing business directly in the east, including Russia, for decades.

I'm sure a few Russian billionaires exert some political pressure in Vienna. Austria is not nearly as politically corrupt as (for example) the US regarding donors. The real reason is the energy market and Austria's large number of eastern European business interests.