There are several different Forstener bit designs. The ones with the smooth sides, no teeth are sharpened with a small triangular file just on the cutting edge, not around the perimeter. These are not the best choice for your task. Forstener bits aren't great for hand held drills, better in a press.
Plywood studs? Maybe laminated studs or plywood gussets, just use an inexpensive, ordinary paddle bit.
Your eyes are the best at determining if anything is sharp or unusable. Have a good overhead light and look directly on the edge that should be sharp. It doesn't matter if it's a handsaw, chisel, drill bit or whatever. You should not see any dings or light reflecting off a sharp edge.