So Hitler was a communist/socialist (and not a fascist) because he “self-identified” as a socialist via the National Socialist Party?
That would be overly simplistic. Don’t forget East Germany called itself a Democratic Republic, as does North Korea.
At the time, Hitler claimed to be and was widely considered a man of the left. The main difference and split on the Left was between National Socialists such as Hitler, and Mussolini; and International Socialists such as Stalin. Hitler focused more on race; Stalin more on class.
Fascism has always been a movement of the Left. It is one of the great lies pedaled after WWII that Fascism is on the Right.