for me, it feel part of the problem steam from way too wide definition of socialism (some are so wide imperial japan could fit) and another is being a contrarian. Another is taking hitler words as more reliable than they really are, the guy in interviews can still say things for propaganda reason per example. The party having socialist in its name also doesn’t make its ideology socialism.
The Nazi’s called their party the NSDAP, National Socialistische Deutschmark Arbeiters Partei (National Socialist German Labour Party). besides that the NSDAP made campaign promises that were similar to socialist policies and favoured more government involvement in the economy. That are reasons for calling it socialist.
Personally, I disagree with the idea that Nazism is a form of Socialism, because of the fact that racism is the essential core principle of Nazism, while any ‘Socialist’ policies of them had a much lower priority.
I don’t regard Bashar Al Assad as a Socialist, despite the fact that his party is named the ‘Arab Socialist Ba’ath Party – Syria Region’.
The term “socialism” has had many definitions and whether you agree to them depends on your politics and sacred cow. Forms of government tend to be who controls the assets of a society and how they are implemented. How you get the people to agree to go along and follow it is where the methods of control and motivations are implemented.
The Economics is in a range of Capitalism where the owners control the assets (Capital) and outputs in a society based on demand to Socialism whereby the government (Social) owns the assets and then determines the outputs based on their direction based on what they say is needed. Then there is communism whereby the state owns the assets and controls outputs eventually to everyone based on their needs. There is also Fascism where the assets were privately owned but directed the output.
Nazism would have been on the spectrum between the socialist to communist economically. They got buy in from their adherents from Nationalism, (supremacy of the state), racism (class separation into superiority and inferiority) and terror (Gestapo, informants/ denunciation, etc)
There is a lot of propaganda the nazis put out that is still believed. Racism was not a primary revelation as the people ware more interested in economic stability. The racism later was elevated higher and was not universally supported by the people, like my grandparents. (My grandfather was denounced at the end of war but was able to hide for several weeks before the US entered Munich)
Traditionally governance types are categorized by economic systems and control of the production.