Ugh yeah I got a partial tear to my supraspinatus a while back... somewhere around 18-24 months ago. Happened doing heavy incline presses on a shitty Smith machine and one side came loose from the bottom while pressing explosively. I could tell it was jacked right away, some odd pain and a weird ripping sensation in my shoulder when it happened, which got progressively worse until the next day when I couldn't move it. Verified via MRI. The VA of course wouldn't do anything for it because it wasn't completely torn.
Took about 8 weeks before I could start rehabbing it with band work. No upper body work at all during that time. Legs 3x weekly lol. I immediately started 3iu GH daily, and I think that sped up the recovery quite a bit. Once I got it moving again and rehabbed a little, I started doing really light work that didn't hurt it directly and gradually increased over time until I got to where I could press light weight without pain. Then I started adding the weight faster as it allowed me to. It's still jacked to this day, and I still can't do pullups or anything where I stretch overhead too far without knocking it out for a week. I know it's going to tear off at some point but I'll cross that bridge when I get there.
One thing that's really important is to keep it as flexible as possible. I let my flexibility slip too much and I think that's why it never healed as good as it should have. I think if I'd have used a percussion massager and did more stretching work it would have done much better. Also some massage work/ART would've helped too I think. So keep that in mind when you get to the point where you can start rehabbing it. Just go easy and don't push it too hard out of the gate or you'll regret it. Stretch as often/as far as you can without causing actual pain. Keep your PT appointments if you go to one lol.
Best of luck to you in your recovery