" By the way, Nazis were the National SOCIALIST party. They were by definition a left-leaning organization."
That's entirely factually incorrect, I’m guessing Nazi history isn’t something you particularly delved into?
To begin with, it’s like North Korea calling themselves the Democratic Peoples Republic. Sure, they’ve called themselves that, but I’m pretty dubious about how democratic it really is.
On a second point, there was a socialist party, and they were entirely at odds with the Nazi Party. In a similar way to how a “democracy party” might be at odds with the governing party in the DPRK. Sufficient to say, they were not friends.
On a third point of the actual voter base that was pursued, one of the major reasons they were embraced was because their voter base saw it as an enemy of and an alternative to the political left, they appealed to working-class resentments to create their voter base (does that sound familiar? Hello 2016 Michigan Wisconsin and Pennsylvania!).
Policy wise, whilst they had a quasi-Marxist rejection of free markets (again, hello Trump market isolationist tariffs and policies!), you’ll find that instead of controlling production or redistributing wealth, the Nazis focused on safeguarding a social and racial hierarchy - so the “large government” was based on nationalism policy, not socialistic policy.
A better term to describe it is “totalitarian” because they were nothing close to socialistic.
Ironically, the Trumpian republicans pursue a closer nationalistic socialist policy platform than any Scandinavian socialist states.