I wonder how much rooftop space in Vienna could be cannibalized for solar panels.

I think your calculations are off. I think that you're including the number for everything including manufacturing etc.

If you're just powering a home, the average American household averages around 11 megawatt.

https://www.eia.gov/tools/faqs/faq.php?id=97&t=3

Imagine how far down they would have to drill to find oil in Vienna, though.

Imagine how deep the mine would have to be to find coal under Vienna.

So combine it with other renewable energy, you know, how it's usually done.

Vienna isn't even the worst place for solar power. Consider places like Ireland, Scotland or Sweden for example. No wonder why wind, hydro or even tidal power suddenly begins to make a lot more sense. IMO, solar really begins to make sense in Spain, Italy, Greece and Turkey. Those places actually get some decent sunshine. Using solar power in Austria should be ok, but it's not great by any means.

Nearby mountains probably get in the way of building large solar facilities. Maybe you could combine solar power with farming. The panels can provide some shade to more sensitive plants.
See also: Solar Atlas
Sidenote: Iceland and the northern half of Norway, Sweden and Finland aren't even on the map. I guess Solar Atlas is trying to tell you that you don't need a fancy map to know that building solar in places like that is a waste of money.

Does it need to be in the city, though?

Also for reference from Google ai: For global electricity needs: An area of approximately 40,000 to 55,000 square kilometers (about 15,000 to 21,000 square miles) could theoretically generate the world's total electricity consumption. This is less than 1% of the total land area of the United States. For total global energy needs: The estimated area is around 497,000 square kilometers (about 192,000 square miles), roughly the size of Spain. This covers the total projected energy demands, including converting non-electric needs (like transport fuel) to solar-generated power.