The national socialists considered themselves right-wing. While their agenda was populist, radical, revolutionary, it’s also anti-left and explicitly opposed to the (left-wing) socialists and communists. Fascists adopted marching and sloganeering tactics from the left but their message was aimed at persuading right-wingers, monarchists, religious believers, etc, who weren’t interested in communism or socialism.
When you look at the electoral history of the period, as they rose the Nazis took the most votes from the Nationalists and National Liberals (eg, conservative, protestant, capitalist funded) as well as the Center (Catholic). People who formerly supported these right-leaning parties converted to national socialism.
The Nazis eventually formed a coalition with Nationalist and Center politicians. As far as I’m aware, the Nazis didn’t form working relationships with “left” parties like the SPD, KPD etc.
They were “right-wing” within their own context–perhaps many aspects of the 30s would be considered “left-wing” by the MSM today.
The 30s were a period of bureaucratic collectivism worldwide–all Western governments of the period shared some common features, from right-wing to left-wing to any-wing. Nazi Germany was particularly barbaric but Stalin set the stage for it.
‘Left/right’ designations more accurately refer to cultural attitudes than economic philosophy. Attitudes towards religion, morality, tradition, authority etc. The Nazis did not present themselves as “secular” the way a leftist party would.