This was good information and good research, and well written. However. Your point, if I can summarize, is that Hitler's economy was a heavily planned economy, and the Nazi party had the word "Socialist" in its title, therefore Hitler's Germany was a socialist nation. Which would add strength to the argument that socialism is bad.
But that is an incorrect interpretation. There was nothing socialist about Germany.
Here is a more succinct and apropos description of Hitler's Germany:
Definition of fascism
1often capitalized : a political philosophy, movement, or regime (such as that of the Fascisti) that exalts nation and often race above the individual and that stands for a centralized autocratic government headed by a dictatorial leader, severe economic and social regimentation, and forcible suppression of opposition.
Hitler's Germany was completely fascist. Don't try to gaslight readers by calling it socialist. That is dishonest.