If you're having problems holding the bar with squats, I'd suggest you start slowly working on mobility in your shoulder, alongside the strengthening.
It happened the same with me, it was inconclusive on MRIs, but looked more like a minor-medium tear of the supraspinatus. I started with paddling my surfboard around for lightweight shoulder rotation strengthening, alongside scapular wall slides and shoulder dislocates for mobility, and those helped a huge amount, and then handstand and iron cross work on the gymnastics rings after a few months took away the rest of the pain and made my shoulders feel incredibly strong compared to pre-injury.
This video shows the scapular wall slide. The only thing to be changed is her lower back is arched out a bit from the wall, and you want to instead try to keep your lower back fairly flat against the wall as you raise your arms.
The other great shoulder mobility exercise that would be directly applicable is shoulder dislocates. I'd be really careful with this one, and not push it too hard, don't go to the point of pain, minor discomfort and tightness will happen at first, but no pain. Just make sure you go wide enough. Here's a great video on them.