If I were rounding up examples of psionic/magic abilities in science fiction or speculative literature, I would definitely tag Dune. Dune draws on a lot of mysticism. How is the Water of Life purified in the body? Basically magic. We're not given a lick of science mumbo jumbo for it. There's the Voice, which is basically magic. There is the Other Memory, which is a mystical Akashic memory for the bloodline. There is precognition and human lie detectors who can sense these things with their minds. Bene Gesserits who are referred to as "witches" and "sorceresses" due to their powers. Sure, not everything that can be explained is necessarily "magic," but it's not exactly trying to be hard sci-fi here.
That's really more the distinction between hard sci-fi and soft sci-fi, not sci-fi and fantasy.
Hard sci-fi: Everything is explainable using known or theoretical science, and probably explicitly explained.
Soft sci-fi: A lot of the technical explanations are hand-waved, but anything done that isn't based on known technology is still assumed to be based on some sort of science. Some re-brand this as Science Fantasy because it's not "true" science.
There's also distinctions between hard magic systems and soft magic systems, although magic in general is optional (though common) in a fantasy setting.
Hard magic: The rules for magic are provided, and any new magic that shows up must follow those rules.
Soft magic: Rules for what magic is possible are only defined by what the characters in the story do.
The distinction between hard sci-fi and soft sci-fi, compared to hard magic vs soft magic, is very similar. The "hard" version provides the rules that define what is possible to the reader, and the reader could extrapolate what is or is not possible without needing to read more of the story. The "soft" version, however, only provides the effects that are used in-universe, and thus the reader can only know what is possible based on what has been done in the story.
2001: A Space Odessey is hard sci-fi. The rules for space travel, and how one interacts with the environment, are all spelled out based on our known understanding of physics. The one element that isn't strictly understandable is
explicitly not understandable by humans. Star Trek is soft sci-fi. Warp technology, for example, is only known after the fact; we can't extrapolate it based on real-world, or even in-story rules. Thus, warp is a thing that can be done solely because we have been shown that it is a thing that can be done, and the limits of how it works are only known once we see such limits in story.
Star Wars is soft sci-fi, or science fantasy. The limits of the force, light sabers, hyperspace travel, etc, are only defined based on what we see in-story, not based on any particular rules. Though that doesn't prevent people from developing rules that they expect to be followed, based on what has been presented, and being upset when those rules are broken (see the sequel trilogy).
The Alex Verus series is urban fantasy using a hard magic system. The Harry Potter series is fantasy using a soft magic system. (Aside: "urban" fantasy takes place in the 'real' world; Harry Potter's world is theoretically modern, but sort of alongside the "real" world, so doesn't really count as urban fantasy.)
The distinction between sci-fi and fantasy thus largely comes down to what it is that defines the "rules" of the setting. If it's predominantly science, then it's sci-fi. If it's predominantly magic, then it's fantasy. Supernatural creatures like vampires and werewolves are a fantasy trope because their very existence depends on magic. However aliens, or nanotech-vampires, would be sci-fi.
It all depends on the justification used for the existence of the supra-normal elements of the story. Enlil and Enki the gods would be a fantasy setting. Enlil and Enki the aliens who crashed their spaceship on earth, but are worshipped as gods, would be sci-fi.
I have a hard time divorcing psionics from the sci-fi side of things, likely because it's based on the same root words as give us things like bionics or cryonic or cybernetics. The word itself evokes the idea of science, and particularly of artificially grafted (or possibly, evolved) powers. While it's rare to have in the same setting as magic, they are not mutually exclusive options. Psionics could be an attempt to artificially or rapidly boost power, as an alternative to the longer process of learning magic. It just fits better in a world where magic is fading, or no longer exists (and thus the introduction of psionics carries a secondary implication of the decline of magic).
