Among the more obvious things, displaced the focus on levelling social and class heirarchy with imposition of the heirarchical doctrine of Führerprinzip, and abandoning any substantive pursuit of the platform plank for confiscation of all non-labor income, and maintaining a robust insistence on the importance of private property and private initiative in industry.

Communists were globalist socialists, Nazis are nationalist socialist. The imposition of the Führerprinzip was pulling power away from the global political regimes supported by the communists into the German one. It's nearly irrelevant with respect to the socialist bit, it's all about the globalist vs nationalist.

>and abandoning any substantive pursuit of the platform plank for confiscation of all non-labor income

What do you think the killing of all those Jews was about? The Jews were stereotypically the wealthy bankers, the 1%ers in today's parlance. One of the first things Hitler did after taking power was run around killing all the communists. Why? Because he believed that the communists wanted to turn over power to international finance regimes (Jewish 1%ers). Obviously the murdering and the racism bits are the key factors for why we hate the Nazis. But murdering and racism aren't what determines whether something is socialist. This was definitely socialism implemented through the eye of a racist.

I'll grant you that Hitler was a hair to the right of Stalin. There was a ghost of private property ownership but the substantive powers of property ownership were held by the government, not by private owners. The government determined what was to be produced, in what quantity, by what methods, and to whom it was distributed, as well as what prices could be charged and what wages would be paid. Does that sound like private property ownership or capitalism or a free market to you? It certainly doesn't sound like it to me.