How do rest days work?

I’ve always been told to workout 3x a week. Upper push, upper pull, and lower body. Resting in between and doing 15 - 30 min of cardio. My goal is to gain but training upper body in those categories once a week doesn’t seem like a lot. Does it make sense to increase the frequency to upper pull and upper push each twice a week? How many rest days is not enough? Do you have to rest your ENTIRE body on a rest day or just a muscle group?