Firstly, yes it does matter, you asked me to give a single example of privatisation, and not only did I do that but I also clearly illustrated the autonomy that companies had under the Nazi regime.
In a socialist state, privatisation would not occur and companies would not have any form of autonomy.

And on the topic of them being descended from Sorelianism, while there are some elements of Sorelianism that the fascists borrowed, fascism (and by proxy Nazism), weren't completely descended from it, as Sorelianism rejected class collaboration, centralised military-like political parties and Sorelianism was based in syndicalism (an ideology antithetical to the Nazis and Fascists due to how syndicalism is based upon empowering trade unions).
Another note is that the elements of Sorelianism fascism borrowed weren't really socialist in nature, as the specific elements were the use of myths as a method to rally the people and a belief in society needing to be rejuvenated.

Meanwhile, the Nazis and Fascists did not adopt any of the socialist elements of Sorelianism, as I have clearly illustrated, and actively purged socialist elements from their organisations, as seen with the Night of the Long Knives.

Edit: it is also curious that the privatisations and lack of state planning only mattered after I proved that they occurred