You are correct. There was certainly a “socialist” component to Nazi German. (But so what?)
However, once this is established, conservatives start frothing at the mouth, and continue with their frenzied liberals = socialists = fascists = communists equation. Because 1890s Gilded Age laissez-faire capitalism is best capitalism.
Certainly Nazi Germany was continuing past Weimar policy, but, by doing so, it became Nazi policy. (Its not like 1933 was a democratic transition. It was a democratic coup. If the Nazis didn’t like a program, it would’ve been abruptly halted.)
Additionally, Nazis implemented programs of their own: eg, Strength Through Joy, a subsidized touristic program.
That’s conservatives’ modus operandi. Somehow, Communists and Nazis both exemplify extreme socialist/leftist ideology. National Review hack Jonah Goldberg wrote an entire fallacious book on this, Liberal Fascism.