There's plenty of stuff that might as well be magic in Star Trek, from telepathy to extradimensional quasi-deities. They just don't call them "magic", and they approach them with an Enlightenment perspective rather than a Romantic one. The whole conflict between Picard and Q is basically a SF protagonist declining to be impressed by a fantasy character. It's that attitude that makes Star Trek science fiction, not some metric of what is scientifically possible. Tons of science fiction is based on positing something impossible and then thinking through the consequences. (Hell, if I wanted to nitpick, even such Star Trek staples as warp drives, transporters, and replicators are flatly impossible as far as current science is able to determine. "Heisenberg compensators" = "a wizard did it".)
Very few things in Trek are lacking in any scientific basis. From Q to Warp Drives, it's all stuff we know might be possible, but are varying degrees of removal away from testing for/developing further than the theoretical. Theoretical=\=impossible, or magical.
Science is what makes a given work of speculative fiction science fiction, while the fantastical and wondrous make a work fantasy. Combining those can make something both, or not, depending on presentation, mostly.
Mall of which is part of a nit pickey tangent that has nothing to do with the setting I proposed, since absolutely nothing about that proposal even requires any lack of mystery and wonder. The common man being able to draw basic glyphs to cool a box full of food or heat a pot (or reservoir) of water doesn't make a setting "not fantasy", but even if it did (and it definately doesn't), that element of a setting doesn't preclude the elements that you insist are what make Eberron a fantasy setting.
A world where physical magic follows rules, where magically created fire still follows the same laws as mundane Fire, except as acted upon by magic, and where magic is studied at the same schools as physics and chemistry, can still have gods and tree spirits and prophecies. And either way, isn't any less a fantasy setting than one where magic is unknowable and even guys like Modenkeinen are basically just guessing, apparently.
Note, I roll my eyes at this idea of wizards not really understanding how spells work. IMO, it is 100% nonsensical. Arcane magic is predictable, follows hard and fast rules, and can be mastered and advanced through rigorous analytical study. The fact that sorcerers and warlocks don't have to is irrelevant. A wizard can study their magic and go, "yeah, that is the same fireball spell I cast, your body is just replacing the material components with an exertion of will and physical energy. Fastinating!" And then go into a rant about the mechanics of energy manipulation to create the fireball effect.
Warlocks are a similar case, except by the core fluff their spells come from a patron, so they've no need to actually understand them any more than a gunslinger need understand gunpowder in order to shoot people well.
As for bards, they go to college to learn most of their magic. Said magic is just as predictable and based on solid rules as wizardry.
Re: Harry Potter. My eyes are starting to hurt. HP magic is entirely scientific. It works on knowable laws/principles, and can be mastered through rigorous analytical study, and advances all the time due to said study. There is plenty they don't yet understand, and knowledge that has been lost to time, because there didn't used to be schools and careful records.
There is no reason to beleive that any artifact in the world couldn't be replicated with the same knowledge that was used to make it, barring a need for circumstances that no longer exist, or happy infrequently, etc. all of it is knowable, just as all of physics is knowable. In both cases, not all of it is known, but unknown=\=unknowable.
