I'll be going there again in a few weeks so I'll report on the breakfast situation. The last time I was there a whole orchestra was staying there because they had a concert at the Konzerthaus. They all came to breakfast at the same time, so the restaurant got full very quickly. Luckily, they had to leave at 8 AM and after they left, the restaurant was mostly empty.

Now I see that there's another concert when I'm there in October so I'm expecting the same scenario. Hopefully I'll be able to find a table.