Somebody wrote:

I have used 3/4 inch plywood for "french cleats" using 3" drywall
screws with a fender washer. Putting the screws into studs I think you
will be ok, just span two studs minimum.

Personally, have absolutely no faith using drywall screws in a load
bearing application.

I like #14, coarse thread, self tapping, pan head, sheet metal screws,
at least 2-1/2" long complete with with fender washers to spread the load.

SFWIW, #14 screw is about 1/4" thread OD.

Use a 3/16" pilot hole drill, drive them with a screw gun, and you are
good to go.

Lew