Sometimes I think using an exact analog of existing firearms is a crutch for the writer or artist. In chapter 10 they just go with 'compressed air' in the bullet, after use the shells are considered 'broken' and return to base components like the airplane did. If you were using wind to create a firearm like weapon you would probably want a completely different design. But this did lead me down a rabbit hole of air powered full sized arms.
1 FPE - Airsoft Pellet
1175 FPE - .223
1500 FPE - AK-47
There is a 1500 FPE air powered rifle, but it needs .72 caliber to be large enough for air to work to get the volume of air needed to move the mass fast enough. And it need 300 BAR, or 4351 PSI, to do that. So your magic would need to trap a LOT of air pressure into a tiny container and hold it without bursting. And the 'strike' would need to trigger releasing that pressure. And you would need to trap the air in the case before you added the projectile. So hand loading only? Unless they just go with 'building magic' to explain it away.
An anti-magic field would cause the air trapped to expand and all the ammo to misfire and probably kill everyone.
A mass producible weapon that anyone can use that can be handed out to low skilled practitioners is crossbows * 1000 when it comes to destroying the existing system? Power to the people, viva la revolution!