I'm trying to figure out if someone is arguing that this proves the Nazis were socialists that this is published on Substack?
This is why it isn't all that helpful to base political ideologies on history farther back than one human lifetime. The writers often meant something different than you think they did.
Your mixing up of the two concepts is wrong and unhelpful. Certainly, the Soviet State was fascist in many aspects. But many fascist states emerge from capitalist economies, with help from the capitalist class.
Context, as always, matters. The Nazis were not socialist, they were infamously and violently anti-socialist. The reason "socialist" was in the name was that Hitler wanted to reframe the concept of socialism around nationalist and racist tenets.
Hitler himself explained his rationale in a magazine interview[0,1]:
“Socialism is the science of dealing with the common wealth. Communism is not Socialism. Marxism is not
Socialism. The Marxians have stolen the term and confused its meaning. I shall take Socialism away from
the Socialists.
Socialism, unlike Marxism, does not repudiate private property. Unlike Marxism, it involves no negation
of personality, and unlike Marxism, it is patriotic... We are not internationalists. Our socialism is
national. We demand the fulfillment of the just claims of the productive classes by the state on the
basis of race solidarity. To us state and race are one.”