A body shop works on car that have been involved in accidents.
But do they also employ a full time mechanic to do example work on brakes,
Suspension, etc.?

Our body shop has to farm their work to us (dealer) for wheels, suspension, alignment. They don't even have a tire machine!
So it just depends what and where.
If the shop has no dealer attached to it, then most likely that body shop will have all the equipment and techs trained in all areas.
But 99% of them don't have the diagnostic abilities, to repair the check engine lights, ABS, and airbag lights caused by the wreck.

Note to Hybrid owners: Stop wrecking them!! Lol.

I think it depends on what a particular shop chooses to offer, but in my locality, no, those auto trades are usually different businesses. The body shop may have suspension people, but they likely only do repairs. A shop that could handle all aspects of car repair and maintenance would be one heck of a shop requiring extensive investment in tools, numerous personnel with different skillsets, and facilities.

There is no "one" rule, Some shops are large shops with 20 plus employees and may have areas that do all sort of work.

But in general most body shops do just that body work only and any mechanic work is sent to another shop