I'm not sure how one would classify , say, Eastern mysticism as "psychic" without Victorian eroticism.
Please explain the coexisting "magic" and "psionics" in pre-Victorian, non-European parlance. Because as far as I have ever encountered, the difference between what can be called "magic" broadly and "psychic power" is purely a modern (Victorian) invention.
Just throwing that out there, not that I expect you to read it. But lemme try to put it another way:
In Sumerian myth, there is no "Magic". Only Power. The Gods had power, monsters had power, and some mortals had power. Inanna, Goddess of Love and War, had the power to turn men into women and women into men, to bring the storms, to encourage plants to grow. To do practically whatever she wanted because she was the Queen of Heaven. And we know this because sometime around 3,000 BCE, Enheduanna wrote a hymn syncretizing Inanna to the Assyrian goddess Ishtar when her father Sargon founded the Akkadian empire.
In the myth of her escape from the underworld ruled by her sister, Ereshkigal, she grants power to Assushumanir, the first nonbinary person to exist, to possess foresight and great fortune or luck. Is that a D&D God handing down Magic to a worshipper, or is it Inanna granting Assushunamir psionics, or is it just the goddess granting power with no special delineation as to the specific name of that power?
We can retroactively call it Magic or Psionics or Whatever term we want... but they did not consider it "Magic" because Magic as a concept wouldn't exist for another 2,000 years when the Old Persian language came around with the term "magush" which meant "To have" or "To be able to use" Power. Because, again, the Old Persian language did not have a word for "Magic".
So is "Magic" just "Power"? Power is the older word, after all. (Technically the older word is EMUQ, which we've translated as 'Power' because it's also used to describe physical strength)
Herein lies the central problem with the question: No one can provide you with what you're demanding because you're demanding a specific linguistic term (and child terms) to be applied to conceits that exist in societies without them. Hell, "Magic" didn't exist in most societies until after it was introduced as a concept to them by the Western World. And regional terms have been translated to mean or be equivalent to "Magic" independent of the actual definition of the word within a given language because it's the closest linguistic approximate when translating to English.
When Buddhist monks in Tibet describe the power they can gain through meditation it's generally referred to as "Spiritual" power. And within their language and society that doesn't mean "Magic" it just means the power of the spirit, the inner self, to perceive the world as it truly is. Is that "Magic" because it's the word we have and use for that sort of thing?
But in the modern day we comfortably say Inanna was magic because she's a supernatural mythical entity. And we comfortably say that she grants Assushunamir magic because it's a supernatural power. And what is "Supernatural" but Magic by another name, right?
And what is Magic but Psionics by an earlier, more primitive, term..? What is the "Supernatural" but the Paranormal by a less accurate moniker? After all, if it exists in the world it cannot be "Supernatural" for it is, indeed, part of the reality of that world, the foundations of Nature, itself.
And around and around and around we go.
The world is more interesting when there's more than "Just Magic". Even if the definition of magic can be stretched to cover everything.