orbital mirrors make very poor weapons because Conservation of Etendue means you fundamentally cannot concentrate very high unless your fill factor is very high (which would require millions of tons in orbit). Lasers are far more effective as weapons as a single aperture launched on a single rocket is sufficient to get high concentration. Microwaves also.
The military application would just be illumination.
Not every possible thing has real situations where it's better. There are legitimately terrible solutions to problems, that are dominated by better ones in every situation.