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As nonsensical as it is, giving the limit of the suspension of believe necessary to keep the world reasonably coherent, the wizard world has a solid grasp on the non-magical world while it's a given (literally a given, it makes no sense otherwise) that the people from the normal world have no idea magic exists, other than what is leaked and relegated to fairy tales (it's our world).
Wizards, their institution and governments, their own citizen are aware of what weapons are. Harry himself of course knows what a gun is and could potentially grab a number of them to prepare for war.
So it's an implied obvious implicit answer that even a limited mastery of magic vastly overpowers weapons. Which is obvious if you consider that in the magical world they are aware of the "laws" of physics AND the extra laws of magic.
They just know more about how the world works, how to inflict death and how to protect against harm.
But IIRC that is never implied in the books and it is shown a couple of times that they know very little about technology and being very surprised by stuff like television. Which is very weird given that a non insignificant part of the wizards are from muggle families and lives among muggles.
Whilst I loved the books, as I read I always had this question in my mind about what if the wizards approached magic with a more scientific method and if they integrated with the scientific advancements of the human world.
In that world, magic is a part of science because it's part of the natural world. It just hasn't been discovered by that world's scientists yet.
Harry Potter and The Methods of Rationality, though they do kinda turn him into a demigod
Given that there are governmental departments for interacting with muggles, and qualifications taught at Hogwarts, my assumption was that it was like many other fields of study typical members of the public did know little, but plenty of research exists. How much does the typical person know about nuclear thermodynamics? Not much, and they don't really need to, but that doesn't mean all of humanity knows nothing. Hermione states pretty regularly that the spells protecting Hogwarts protect it from being discovered and prevent electrical communications from functioning.
I would think that, in a war with muggles, any wizard signing up to fight would be given training (by those few governmental and academic experts) in muggle warfare, weaponry, and relevant defensive spells needed for such a conflict.
Yeah, though it's not the best of movies, Disney's The Sorcerer's Apprentice did a really good job of treating that barrier between science and magic with a degree of reason and accountability. And in my own head canon those ideas are part of the Harry Potter universe and it's magic.
and its* magic
I mean they don’t really get taught anything about the outside world. I don’t remember seeing physics or social studies or any other “normal” class on Harry Potter’s class list.
My understanding is that they used wards to prevent technology from working near them.
So in your "canon" no mage ever asks itself why rocks fall to the ground?
I mean it's a possible angle, overreliance on rituals and magic that sapped those people of any critical approach to reality...
I mean it took them forever to get indoor plumbing. The Romans had indoor plumbing.
Harry Potter wizards use magic instead of technology, they don’t really seem to be interested in using both together. So I believe that they don’t go out of their way to understand technology or the physics behind it.
Many magical things defy physics in that world. I think wizards in that universe see science as an obstacle and not a valuable method for understanding reality. Because their reality defies understanding by scientific process. It’s all ritual based. The pronunciation of a spell changes its effect.
It’s not a lack of critical thinking that makes them avoid science. It’s the fact that what they do is more immediately effective than science.
Their reality doesn't defy understanding by the scientific process. It has reliable, repeatable results, and therefore can be studied and empirically catalogued. The only way something could not be studied by science is if it's totally random, if actions do not correlate, even slightly, with results. Of course, such behavior would make it completely useless as a tool, because one could never get desired results from it. Magic in the setting is very reliable and repatable, and as long as you do it right, results can be studied, so it's easily catalogued by the scientific method.
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.
They aren't using it, no, but that doesn't mean the scientific method can't study what they do and come to an understanding of it - probably a better understanding of it than they have, since as you say, they aren't using it. It'd just take a few decades of study probably to have a much stronger understanding of how it works.
My point is just that people draw this weird line between 'science' and 'magic' as though they were incompatible. In a world in which magic is real and useful, science can study it.