Before World War II, Austrians called their country German Austria.
This is not a view held today. Austrians nowadays do not want to be German, they have their own identity.
Before German unification, Germany was a geographical area, not a country. There were many German kingdoms and nations. Austria, had never been united with the German kingdoms to the north, except for limited alliances. It was in the Hapsburg controlled empire. The Austro-Hungarian Empire, running up to the end of WWI, was allied, but quite seperate from Imperial Germany.
About the only thing that Austria and Germany have in common (more so than any other European countries) is language.
If the Austrians wanted to be part of Germany, they would be part of Germany. The only time in history that they have been is 1938-1945.