But let’s be clear, the Nazis didn’t dictate what would be produced
I don’t think left and right matter so much at that level of violence and authoritarianism.

It is not true.

There was a reason why Reichswerke Hermann Goring was taking more and more of steel industry. Krupp and others did not have a choice but to do what the State demanded, and I am not talking about war-time Germany, but what started in 1934, with “Four year plan” etc.

If you wanted to preserve your business, you produced what the government told you to produce.

Socialism is not necessary based on Marxist phraseology. And not all Socialist see immediate nationalisation as the first priority.