You're essentially describing Idealism vs Materialism.
Related is Nietzsche thinking he was the one to overturn Plato. Heidegger thought that Nietzsche was instead the logical conclusion of metaphysics. Heidegger's project was about "returning to the Question of Being" which he thought was first occluded by Plato, so he is in strong conversation with the Pre-Socratics. Deleuze has an interesting critique of Plato built on flipping the latter's hierarchy of model and copy.
> insane forms of magical thinking like [...] where people believe that our thoughts determine reality.
This can't be hand-waved away as easily as you might think.
Yes, those are the proper terms.
Nietzsche was weird. He was not an idealist but he posited this transcendent idea of "will" which is basically New Thought. But I'm not an expert on Nietzsche so maybe there is more nuance here.
There is a kernel of truth to New Thought and its kindred ideas -- if you believe in your future success, you are less likely to become discouraged. In many cases success is claimed by those who are willing to fail over, and over, and over, and over again until they succeed. But that's a brain hack, not metaphysics. Your thoughts have determined your behavior, which has increased your odds of success, which can then be retroactively interpreted as magic if you are so inclined.
As far as hand waving it away -- I think the burden of proof is on those who claim such an extraordinary thing as "our thoughts determine reality." I want to see someone actually bend a spoon without touching it. Then we'll talk.
>But I'm not an expert on Nietzsche so maybe there is more nuance here.
not just more nuance, that's a straight up misreading of Nietzsche. For one Nietzsche rejected any notion of transcendence, free will and was an (idiosyncratic) materialist and not a self help writer. He did not think you could manifest success by believing in it, or even that this mattered.
In fact one of his central ideas, Eternal Recurrence, implies the exact opposite. He argued that you ought to imagine the worst possible state you can be in, recurring over and over and say yes to the world purely out of love of fate, Amor Fati
"My formula for greatness in a human being is amor fati: that one wants nothing to be different, not forward, not backward, not in all eternity. Not merely bear what is necessary, still less conceal it—all idealism is mendacity in the face of what is necessary—but love it"
Will in Nietzsche is immanent, he had nothing to do with New Thought, an as far as I'm aware idealistic American religious movement, he couldnt' be farther away from it if you tried to be honest.
The Will to Power is a complicated concept that can be interpreted many different ways. And actually his whole point was attempting a purely immanent philosophy. WtP is not a transcendent.
The idea of Platonic forms (and rejection of it) is better thought of as the debate between Universalism and Nominalism. Does there exist an perfect, "ideal" representation of a Chair, or is a Chair just a human construct made of it's constituent parts?
Funnily enough, Computer Science is quite platonic, the concept of OOP with classes and instances is pretty much a direct analogy between a platonic form and it's instance, and conceptually we have ideas like the Turing Machine that can be defined as universals that would exist in any culture. In contrast, much of "Continental" Philosophy and the associated Postmodern and Critical Theory movements are very much motivated by the rejection of universalism and the "great other" for a more cynical view of power dynamics shape the discourse of language itself.