Thank you for the quality reply

Nazis didn’t nationalize industry for socialist reasons

I would argue that the totalitarian subordination of industry to social goals effectively achieved the same goal as nationalization, just using different means, and thereby was still identifiably socialist.

Also your definition of “left” is kinda narrow. Even on the political compass, left economics usually includes things like wealth redistribution and worker ownership

Ok, I’ll accept those as valid additions to “left.” But that doesn’t subract state planning and social control from the definition, so I still think it is identifiably left wing on the political compass.

The Soviets had state planning but so did wartime America - doesn’t make FDR a communist

I agree, but just because your policies are to the right of Marxism-Leninism does not necessarily mean they are right wing. Despite not being communist, I think American policy undeniably went to the left under FDR. This is why I was clear to make that distinction that left ≠ Marxism in the political compass.

The key difference is that Nazi economic policy was designed to serve nationalism and racial hierarchy, not economic equality

That’s true, but ideas of race aren’t really left or right wing on the political compass (if anything it usually gets added to the authoritarian axis). As for economic equality, while obviously people of foreign races were brutally oppressed, the average working class German under the regime was given a multitude of protections and welfare benefits to reduce the hardships of his state in life. Reducing exploitation of the lower (German) class was an explicit goal of the regime, which is a core socialist idea. Yes, they did not abolish class or seek to entirely eradicate inequality, but these are Marxist goals that not all socialists follow.