Wheel studs are pressed into place.
To get a broken stud out of disc brake coach:
Remove the rear-side nut.
Press out the broken stud from the rear by pushing outward.
Make a tool that can force the broken thread-end by pressing against the disc brake. Protect the disk brake surface.
A tool could be two short bolts connected with a coupling nut. Or use broken wheel stud threads into one end of coupling nut.
Turning coupling nut extends the tool length exerting movable force on the rear of the wheel stud, pressing it outward.
New wheel stud is pressed (pulled) into place by tightening the rear nut that comes with the new stud.