If I've got my Nietzsche right, then wouldn't the idea of Ubermensch as something you can become rather than something you are not really line up with fascism anyway? Seems like they just took a word that sounded cool if anything.

There's a ton in Nietzsche to support fascism, starting with his virulent hatred of democracy, socialism, and liberalism.

He is simply the most important philosopher for the creation of fascism, including Giovanni Gentile, who gave Mussolini all his ideas.

That's not to say he was a fascist himself, for example he absolutely hated nationalism and that's kind of a requirement, or there isn't any value in his works, I think there's actually a decent amount in there for any kind of attempt at self actualization and rejecting victim mentality, but he's definitely what you might call a proto-fascist thinker.

Keep in mind that there's more kinds of fascist than Nazis. There's even more kinds of Nazi than anti-semitic Nazis.