"One of Nietzsche's central tenets is that pretty much all 'knowledge' and 'belief' is just us projecting our interpretations (rooted in what we would now term cognitive biases, value judgements, sensations, etc) on reality and then "reading" them back to ourselves as the ground truth, which is in fact unknowable as such."
Something which Nietzsche is guilty of himself. But that road leads to postmodernism.
Nietzsche did not claim to hold a privileged position in this regard, nor in his opinion does that position necessarily lead to postmodernism. Indeed Nietzsche would have been mortally offended by the entire postmodern project, the forerunners of which he clearly believed to be inspired by decadence and ressentiment. Nietzsche's "there are no facts, only interpretations" goes much deeper than postmodernist ideas about moral relativism or whatever: Nietzsche denies that there is (or at least that we have the grounds to believe in) any such thing as responsibility, guilt, will, causality, Being, or even identity, both in the personal sense and the logical sense.
His focus instead is that, given the essential failure of metaphysics, to instead try to destroy as many as the 'old idols' rooted in these cognitive biases and value judgements - to see to what extent life could endure the incorporation of small-t truth (Nietzsche suspected that many errors were actually necessary for life) - and to re-evaluate our values with the (arbitrary!) view of increasing the health of the human animal. And he makes clear that this depends on the person: "the exception should not try to become the rule." Nietzsche's philosophy is explicitly not for everyone.
In terms of practical life advice, Nietzsche ends on somewhat common ground with the Stoics -
> 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.
On the contrary, he is claiming to hold a privileged position; not perhaps on the true nature of knowledge, belief, or "ground truth" (although I believe he is doing that, too), but on the ability to determine what is projected interpretation and what isn't. In fact, if he isn't claiming that privileged position, then he is more than halfway to postmodernism; not perhaps denying that such a position is impossible, but at least denying that anyone has (or possibly could) find one.
By the way, one of the difficulties of a philosophy explicitly not for everyone is that it cannot avoid turning into us-versus-them, followed shortly by the wise and knowing versus the misguided, misled, and heathen sheep. One lesson of the 20th century (if it needed teaching again) was that philosophy can be weaponized.
(One nice thing about (my interpretation of) epicureanism and possibly Zhuangzi is that the sheep may be heathens, but I don't need to care.)
Something which Nietzsche is guilty of himself. But that road leads to postmodernism.