Science as a methodology began developing in the real world during the renaissance. Prior to that people had methodologies that provided moderately accurate models of reality but often included superstition, unsupported metaphysics, or religious dogmas. These other inclusions are what we call magic: Alchemy, astrology, geomancy, thaumatergy etc.

Assuming Harry Potter’s world developed similarly to ours, the muggles would have taken a scientific view of reality beginning around the 1500s. But magic was real and wizards kept their magical methodology and metaphysics.

They clearly have learned a lot about magic because they no longer call on demons or need the moon to be in a particular phase, but they aren’t using the scientific method to do that.