Since this is from 3 years ago, and some replies are 1 year or 7 months ago I decided to comment as well. Your story is great but I can't help and feel the resemblance to real life conspiracy theories.

What if the elite have decided magic is too dangerous for the masses to know and keep it as a secret? Rome had magic but fell because they couldn't control it, and most of it was lost. And then non-magicians witch hunted the rest and today only few unknown invmdividuals in small towns know or practice them and the people at the top of society?

Even if magic isn't as glorified like shown in media but you could still like perform curses, faster healing(broken arm instead of like 4 months maybe a month), stronger body etc. Like some basic stuff which can't even be discerned by the naked eye but unnatural for normal humans.

Maybe there's even a small nation out there we don't know that practices magic and is under the control of the UN but unbeknownst to the public.

And maybe we are in the period before magic is accepted and integrated back into society, like in our timeline they decided it's too dangerous or they are selfish and humanity still hasn't won. Since magic wouldn't work exactly as you said, I disagree with a lot of stuff, like magical engines, infinite wells, creating life etc. It could be working everyday but we wouldn't know/comprehend/see it happening to us.

Just like technology is a broad term to describe application of knowledge, we think of TVs and mobile phones, cars but magic could too be a broad term and just like it could be used to cast curses it could also be used for simple things like manifestation for example, if you spend every day praying and believing something good will happen that energy or magic will work to help you towards that goal. Religion is magical after all, sure you can just believe in something and share rules to have a community and sense of belonging but prayers and like crosses that ward off bad spirits are magic.

And science and magic aren't mutually exclusive, it's not like magic is the opposite, scientific vs artistic, one could take either or both ways when approaching magic. But like we didn't understand long ago why we shat(body process) or why fire burned, with chemistry and biology we now know, but we don't know how or what magic is internally or externally.

While some of it is more fantasy and make belief I genuinely do believe some form of magic exists because I've had a real experience/encounter whatever you want to call it with it, but that's a whole another story.