I’m looking for magical girl manga where the girls discover and learn magic by themselves instead of it being granted through some contract

Witch Hat Atelier has girls learning magic by being taught it. It's not really the magical girl genre -- and their mentor is a guy and there are plenty of male witches in the background -- but the overall focus is on a small group of young girls learning magic.

Not sure if that's really what you're looking for, but its at least adjacent! (Also, the art is lovely.)

e: Oh, and there's an upcoming anime of it, here's the trailer