Two 20th-century ideologies promised a utopian vision that would ensure infinite happiness.

Marxism was never rooted in utopianism. Marx distinctly criticized utopian socialism and instead was a rationalist through and through. He believed in cause and effect, and knew that things would always change and evolve. Utopianism on the other hand is rooted in the idea that things can reach a state of perfection and forever remain so, which is directly contrary to the philosophy of Marx.

Fascism, like every other ideology, was influenced by Marxism.

Fascinating, I wasn't aware that every ideology in the history of earth was based on the theories of a man who wasn't even theorizing until the 19th century.

However, Fascism’s roots lay in the right wing of the revolutionary struggles of the 19th century. “National Socialism” is not an entirely inapt name;

The second you admitted fascism is right wing is the second you admitted it can't be a form of socialism. Socialism is far left by definition.

socialism was a broader term for various ideologies and movements that attempted to solve the problem of class conflict

And all of them were left wing, because all of them were based in egalitarian ideals.

fascism sought to solve this

No, they CLAIMED to be trying to solve it, and instead made it worse. What part of "Hitler is a lying scum-fuck" don't you understand?

exhorting workers in marginalized states to join with their respective bourgeoisies against parasitic “international finance capitalists”

This is how fascists gain the support of the left/working class. They lie, and they lie well and often. They also do things to appeal to the right and the wealthy class, but when they get into power even most right wingers are shocked by the right wing evil that ensues.