Yeah, I think that “nationalism” is often associated with the right wing, and “socialism” is associated with the left wing. Nazi, being the “national socialist party” seems to sit right on the fence. Since they built a strong military force, I think that that is why many today seem to associate the Nazi party with the right. However, they were very left-wing at their roots.
I always felt post WWI Treaty of Versailles was used as their source to claim victimhood of Germans (nationalism) (rather than race, gender, etc.)to promote their left wing agenda. And they’re still using victimhood (collectivism) today. Nothing has changed.
Socialism is ALWAYS left. The Nazism is socialism with control of private property via regulation, not by ownership. They are only right wing to the communist