About two years ago I made a similar transition for the same reason, from mostly focusing on compound movements with little isolation to a more bodybuilding style to improve my physique. Now, I start each workout with a compound movement in a lower rep range (low for bodybuilding style, 5-8), but then transition to more into isolation movements and focus on using a weight that allows me to maximize tension in the working muscle, and less focus on how much weight I'm using. this article "Why Bodybuilders Are More Jacked Than Powerlifters", peaked my interest and got me more into bodybuilding, ultimately to the point of competing.
Every four weeks or so I will have a week focused more on strength, including lower rep compound movements, sets of 3-4, and not much isolation work. It is extremely important to keep these lifts in the program and keep improving strength.
I think it's very important to recognize that this is not an "either-or" situation. You don't need to pick between "bro-splits" as you say and lifting heavy. The vast majority of successful bodybuilders all have heavy compound movements in their program, improving strength is an important part of training.
@Aragorn hit a very good point here. Since you have a foundation in strength training, you should be able to make visible progress sooner than later with more bodybuilding style training. I was able to see results pretty quickly, my training buddies could too.
It's also important to note that bodybuilding style doesn't mean "high rep, high volume". The best programs are well rounded, include heavy compound movements and a variety of rep ranges. Some of my sets are 5-8 reps, some 8-10, some 15-20 and then you have drop sets or extended sets sometimes which can total a couple of minutes of TUT.
To answer your question, YES, training in this manner will absolutely add muscle mass and develop your physique. But it will take time and consistency, a well balanced program and very consistent nutrition. You're certainly not wrong that getting stronger will make you bigger, but if you're not doing some higher rep, isolation type movements geared towards hypertrophy, you won't have the physique that your "bro split" buddies do. The best thing I think, if physique improvement is your goal, is to incorporate your strength training into a hypertrophy focused training program.
I VERY highly recommend CT's Indigo Training Programs, the "hypertrophy" program. It's an incredible combination of strength and hypertrophy, and every workout starts out with compound lifts. Here are the programs.