I don’t think left and right matter so much at that level of violence and authoritarianism. The lived experience of Germans and Russians (from non-persecuted groups) wasn’t so different. The regimes’ methods were ridiculously similar.
But let’s be clear, the Nazis didn’t dictate what would be produced. They didn’t have to. They dictated what they would buy. If Krupps wouldn’t make it, another company would. There was competition in their system. And that control you talk about was far more diffuse than in a centrally planned socialist system.
Look at the KZ system. Himmler and the SS used prisoner slave labour to make uniforms and war materials.
They sold those back to the armaments ministry at a profit. And used the money to further finance the SS at all levels.
All that is not socialism in the red sense. That kind of cooperation between corporations, owners and authoritarian government is fascism.