Then they killed most of their leftist elements
I didn’t address them as left or right wing.

Nothing unusual for left-wing dictatorships to kill left-wing elements in their parties.

Communists in Soviet Russia were well known for exactly that.

As for not nationalising companies immediately as they came to power, it is quite common. Socialist Party in France was in power, and they still had private companies. And today’s Syriza in Greece — they did not jump immediately to nationalise everything.

National Socialist definitely when much further then many European Socialist parties. They put all industry under government control. On paper the large companies might still be private, but in reality they were strictly controlled by the State which decided what exactly needed to be produced, so de facto they nationalised all those companies.

And yes, they were enemies of liberty. The same way as many left-wingers are enemies of liberty.

In terms of liberty today it is the so-called “anti-fascists” and “liberals” (in modern American meaning of this world) that are the most authoritarian.