Bingo. My own experience has been that to improve your bench (and military press), you need a strong back. Without even opening the muscular balance can of worms, I’ve found I need to train my back twice as much as my pressing muscles to get any kind of progress on my pressing, EVEN WITH working on technique. It’s way, waaaaaay easier to lock your shoulders in and stabilise everything with a stronger back.
TL;DR hit pull-ups, barbell rows, lat pulldowns, dumbbell rows and pull aparts really hard and often.