A "supernatural" explanation appeals to ontologically basic mental things, mental entities that cannot be reduced to nonmental entities.

I think there are supposed to be non mental "supernatural" artifacts as well. Like Thor's hammer.

I find "miracles" and "supernatural" basically placeholders for "we don't follow the rules". It's basically magic. Harry and I still think there would be rules, just new ones.

In the context of the OP, I think miracles are "magic from an entity". He wills it, it is done. The miraculous part isn't the ontologically basic mental thing, but the lack of understanding of how the ontologically mental thing can produce physical effects.