re: People always assume “magic” is ultimately explained by science. Is that wrong?

As others have said, magic and science have always been linked.

Would be alchemists and the priest class of earlier societies were often the scientists of their day, with science more formally splitting away from religion... I forget when... maybe the Renaissance or Enlightenment? But there's always been mutual influence. For instance, highly regarded people in esoteric and occult circles, like the Renaissance era Paracelsus, have made huge contributions to the scientific world and medicine. Likewise, highly regarded scientists like Isaac Newton delved deeply into esoteric work. Newton did a ton of work related to alchemy and esoteric bible study, from which he made a lot of prophecies, including the end of the world... sometime around 2040 (for which we're arguably pretty well on track).

I'm very strongly Christian, though I also hold a strong Platonic worldview, and generally see reality as a heirarchy of layers-- basically The Great Chain of Being, for which Plato and Aristotle are generally considered the forefathers (google The Great Chain of Being if you're not familiar, as this is a topic for another thread). This is relevant to your question. Essentially, there is a network of relationships between all things; everything that is and everything that can be done (via magic, science, the will, etc.) will in some ways be explainable through this network of parallel and heirarchical relationships. To the extent we don't know and understand, we're just more inclined to ascribe it to magic vs science from a point of ignorance.

To your example... what if someone in some remote village with hepatitis B-- in a bizarre act of masturbation and desperation-- shoved a carnation up their arse, and somehow (seemingly magically) became cured. Maybe the residing shaman / witch doctor / priest takes note and tries it out on someone else who approaches him for help with hepatitis B, maybe dressing up the act up ceremonially with specific prayers and times it for the full or new moon. Say it works, and has a high success rate. Now we have a seemingly magical procedure.

Years later, it's discovered that carnations are naturally high in vitamin C, or iodine, or some unique anti-oxidant that is effective against hep B (I'm making this up, no clue). And it turns out that by taking it up the arse, you absorb these nutrients better than by consuming them where stomach acid destroys the nutrients. This wouldn't be unreasonable considering people have chugged liquor rectally to get drunk. Further, what if the subtle energetic effects pertaining to the position of the sun and moon do provide a subtle boost (or hindrance) to the electro-chemical process of the the nutrients interacting with the body. Again, this isn't completely unreasonable considering that the sun and moon have significant energetic and gravitational effects observable in the tides. And there you have it: science has explained your hypothesis of carnations up the arse curing hepatitis.

To be clear, I'm not dismissing "magic" as inferior to science. I'm saying that I still see the two concepts linked deeply. What is called magic is not completely incomprehensible, but requires a deep understanding of the laws of the universe, of rhythms and dualities/polarities (male/female, electric/magnetic, hot/cold, etc.); and understanding affinities and correspondences between substances that amplify effect.

Science and magic are both just words that generally point to processes and outcomes from a different perspective. If either word wins the ultimate battle of usage, do they change the processes? I'd argue no.

I realize there are deeper levels to this question pertaining to the potentials of the mind and will independent of matter. (Look to the biologist Rupert Sheldrake's work on morphic resonance, for example; or to the wide array of topics/guests on parapsychologist Jeffrey Mishlove's New Thinking Allowed podcast.) But I'd suggest even these more esoteric topics are governed by laws that we just don't quite understand from our current perspective.