Pretty much every 'magic-like' effect we see Garleans pull are technology, most often apparently from augmented weaponry or armor. Basically, they're going in as Iron Man and hoping that holds up.
Out of these, the biggest ask--but also the biggest tell--is Gaius. It's not an impossible ask, he'd just have to have one hell of a setup hidden away somewhere in the Praetorium to justify a fight like that. However, later on in Shadowbringers we see him with confirmably little technology through armor (and arena setup), showing that everything he uses in those cutscenes are entirely powered by the one piece of tech he confirmably does have, the Garlean gunblade. (Well, and the bullets.)
There's probably still an element of skill and technique there; you can't just give any Joe bas RandomGarlean Gaius' gunblade and have them pull off the stuff he does. But the 'magic-y' stuff in terms of raw ability to expel those blasts? That's in their tech.
The one other exception is Zenos, who over time showcases four different things to consider about how Garleans like him can stunt:
- He has multiple magic katanas. That's where most of his weird abilities in Stormblood's fights come from.
- He's physically just VERY strong, which is an innate Garlean thing; basically, their aether manipulation is tuned inwards to make them capable of great physical feats, which sounds good, but mostly doesn't manifest as anything that useful. It combined with the magic katanas to mean Zenos could be more than a match for us.
- Remember the Reapers? Yeah, that's an old Garlean way to keep pace. It's not popular anymore, since magitek's just a much safer way to do it, but Zenos doesn't care about safety concerns.
- Finally, Zenos himself gets to be a Very Special Boy, between both the Resonance he gets late in Stormblood and the indistinct magical abilities Elidibus unlocks in his body (that Zenos proceeded to never use). Those aren't exactly normal tricks for Garleans, but they could theoretically say things about them... if Zenos ever said anything to explain either of them particularly well. Sadly, he does not.