The idea that Austrians aren't German is a post-WWII idea. Until 1945, they considered themselves German. And a vast majority supported integration into the German nation-state even before it was formed.
But then Hitler tried to exterminate several different races of people and all of a sudden Austrians decided to become a different ethnicity.
And they're very smart. They've figured out how to make Hitler into a German and Beethoven into an Austrian.
As for Hitler's demise--he was mentally unstable in the extreme (as was Alexander). By 1945, none of his actions had any root in reality (whether "real" or perceived reality).