Try to find a PT who does more than prescribe a few exercises. I had tears 14 months ago (from and ill-advised reach to put something on a high shelf) and it is FINALLY in the last stages of healing.
A good PT can put their hands on you and find exactly where the problem is - the 4 muscles that comprise the "rotator cuff" extend from the shoulder tip across the scapula.
Here is a really good description and image of the rotator cuff muscles and their functions:
https://www.healthline.com/health/bone-health/rotator-cuff-anatomy#treatments
Once the area on my shoulder was healing, another tear was identified deep in the subcapularis. It took months of myofascial & targeted manipulation, with very gentle exercises on my own, to heal. I finally got the "go ahead" to start strengthening exercises two weeks ago, and it is amazing how heavy a 1 lb weight can be with some of the targeted exercises!

So my advice is to find a skilled rehab PT and prepare to work on it - possibly for quite a while. I had great examples many years ago - both of my parents had rotator cuff surgeries in the 1970's and were able to recover full use by diligent exercise.