Why are the brakes slowly engaging on their own after a little while of driving it. 1994 Ford Ranger?

This is usually caused by the master cylinder, the valve that allows the fluid to return will stick. I would try a new master first since you have a warranty and if that does not correct the problem, the booster would be the next step. If the old master was leaking fluid out the back and into the booster it could have damaged the booster. Good luck.