This may work for a little while, but once you start creeping up to a point where recovering from the workload/ weights get closer to Max/adaptation is taking longer you will stall, at least doing 2 heavy days a week of each compound. I’ve stalled multiple times on 1 day of each compound a week due to under recovering (ie undereating, mostly) which it seems like may be the case as well for you if you’re afraid to get fat.
I was also a very skinny kid out of highschool at 6’ 165ish lbs. Tried to stay skinny, ended up just getting a bit fat as time went on. Now I’m 29, and have put on about 25-28lbs in the past two years. A bit of it is fat, but honestly it helps to fill out my frame. Still have some ab definition, definitely not shredded though. I’d highly suggest following Jim’s food recommendations as closely as possible. You’ll for sure gain a lot of muscle and not get fat if you’re working hard enough.
I see you have chosen a program and that’s great. You also may be a good candidate for isdatnuttys beginner program. It’s double progression, highly customizable and higher volume than 531. I gained a good amount of strength and put on some very decent size during my short stint with it, but I underate and had some stressful weeks at work and tried to progress too quickly so I under recovered, and it wasn’t sustainable for me. You might want to check it out as a fallback if 531 doesn’t end up being your thing.