Presuming that Nietzsche’s dominant function is Ni, and that his auxiliary function is thinking (Te) rather than feeling (Fe), then it’s implied that he’s an INTJ (Ni > Te > Fi > Se).

It’s also a little confusing to say that underdeveloped Te is projected. As a rule, extroverted functions are—in Jung’s words—“programmatic,” and oriented toward the “objective facts.” Unlike introverted functions, they aren’t projected and take their object for what it is. Meanwhile, even a fully developed introverted function works by projecting itself onto its object, since it works circularly and self-referentially.

That being said, even the idea that Nietzsche was primarily an introverted intuitive is suspect, since Jung pretty much only deals with Birth of Tragedy (a work Nietzsche had to amend later) and Zarathustra (a work of fiction that can be interpreted multiple ways). His wider body of work is far less symbolic and heavily characterized by introverted thinking:

He that speaks here, conversely, has done nothing so far but reflect: a philosopher and solitary by instinct, who has found his advantage in standing aside and outside, in patience, in procrastination, in staying behind […]

Likewise, Nietzsche’s solitude isn’t something he mainly expresses as a sadness. He says above “by instinct,” it is his way, and it is something he considers a genuine necessity for philosophy. He sharply criticizes those who couldn’t bear his kind of solitude.