Growing up in the 90s in Sweden, we definitively were taught that "Übermensch" ("Övermänniska" in Swedish, literally "Above Human") was something the Nazis promoted during their time, together with demoting "Untermensch". Maybe that's wrong, and if so I thank you for the correction, but "Superhuman" does give me similar vibes regardless, not because of the exact wording, but because of the ideas/concepts.
Nietzsche’s sister tried to garner favor with the Nazi regime. After Nietzsche’s death, she took his notes, published them under the title “Will to Power” and made it all sound as though Hitler was the fulfillment of Nietzschean ideas. Even scholars who built their careers on Nietzschean philosophy fell for this. For example Ayn Rand. So your teachers were in good company. In truth, everything about the Nazis would have made Nietzsche sick to his stomach: group-think, racism, big government, socialism, robbery, personality cult, lack of intellect, mass appeal, Gleichschaltung, militarism.
Elisabeth and Bernhard were rabid nationalists and antisemites long before the NSDAP. They established their vegetarian-antisemitic-'Aryan' colony in Paraguay in 1887, two years before Adolf Hitler was born.
It failed for financial reasons and the rather harsh environment. They ditched the vegetarianism and started selling meat to get some money, spiraling into alcohol and morphine abuse. In 1889 Bernhard killed himself with strychnine, after which Elisabeth started her career as a fake chronicler by writing a book aimed at creating a much nicer and 'Aryan' image of Bernhard and the colony than the truth would have allowed.
As you allude to, Friedrich Nietzsche poured buckets and buckets of abuse over people like his sister and other german nationalists, refusing for the entirety of his life to identify as german, and towards the end of his life he even claimed to be a polish nobleman, free of the tainted blood of the germans.