I think the magic vs technology breakdown is a bit problematic, because the linelines between technology, nature, magic and divine or supernatural entities can be quite blurry, and magic in itself can have varying definitions.
I would rather break it down into natural and supernatural natural and supernatural (which probably roughly corresponds to what you call technology and magic).
By definition, this is all that can exist. Either something is within nature or it is not. Either it is natural or it is supernatural. Well, it could be both, but there can't exist somethinganything besides those 2 things, since the one by definition includes everything the other doesn't.
Natural
Anything that fits squarely into the laws of nature.
This includes:
- Pretty much anything any natural beings are capable of doing or creating. This includes a billion ants getting together and digging through a mountain top as well as a human building a machine to do so.
- Any natural effects (storms, earthquakes, magnetism, etc.).
- Any force or effect by a natural being that only interacts with the natural world. I can use my hand to lift something up. That only interacts with the natural world. This is specifically intended to clarify magic-like forces (e.g. manipulating, observing or creating objects in the natural world purely through our minds). Those would also classify under this category if you were to include them fully within the natural world and give them a natural explanation (as opposed to having them be partially or fully supernatural). This is probably what something like the X-Men (and many modern superhero stories) is going for, where powers are explained as being purely related to physical mutations.
Supernatural
Anything that can manipulate the observable universe, but exists fully or partially outside the observable universe. Things that would violate the physical laws of the nature (not the laws as we know them, but as they exist).
This might include:
The natural drawing from the supernatural: those in the natural world drawing on or possessing forces outside the physical world (i.e. certain interpretations of magic).
Independent supernatural forces: Gods or similar beings. Ghosts may be included here, or they may be considered natural (depending on interpretation).
Manipulating the natural world indirectly: Those in the natural world manipulating the fabric of reality directly (i.e. getting into and changing "the code" of the universe, by e.g. causing a paradox or otherwise "breaking" the universe through natural / technological means). If humans naturally possess this ability, a good argument can be made that this is part of the natural world, they are drawing on the supernatural or they themselves are supernatural (think Neo in The Matrix, who can do "supernatural" things within The Matrix, but arguably only because he had an existence outside of it).
I don't believe there is any supernatural force that would fall outside of all 3 categories mentioned above, as they are very broad and based on the different ways any 2 things A and B can interact with one another (those things being natural and supernatural in this case): A affects B, B affects A or A affects itself. But I might be wrong.
This definition of supernatural might arguably also be problematic, since something's existence and ability to affect the observable universe might necessitate it's inclusion in the laws of the nature, and something doesn't need to be directly observable to be a fundamental part of the laws of nature, but I think it does a good enough job to demonstrate something distinct from what we typically consider to be "natural".