There were many die-hard socialists in the Nazi party, Hitler was more of a pragmatist, in that he wasn’t driven by ideology, he used Capitalism when it was to his benefit, and socialism when it was to his benefit. And anti-semitism was the glue.
There was no real capitalism going on, it was all controlled by the heavy hand of the state. Command Capitalism is not capitalism as I understand it.
You hit the nail on the head.