Do the ordinary lower-class people have any magic?
I think so. I hate the trope where super-special snowflakes can get magic, and everyone else is out of luck. But, still, magocracy is the central trope. . . .
They can do lesser magic. In fact, they can do more useful magic earlier, because they spend less time mastering the power and can get into the subtlies earlier.
I think they are also going to have to have a fair amount of anti-magic. You devise a clockpunk device, you want it to be strong enough to cope with a malicious fracturing spell.