I had the same problem, actually worse since I partially tore supraspinatus, subscapularis, and long head bicep tenton. I was told to have a surgery if I want to continue lifting seriously but so far my shoulder feels way better and most of my strength has returned with physio only.
First of all, I suggest you dont do any movement if it really hurts. I know it sucks, but trust me, a week off is way better than 3 months off.
If you can perform movements without significant pain you should incorporate some external rotations. My physio had me make a variaty of external and internal rotations from various positions, but to keep it simple just perform some external rotations of a kind. 5 sets of 10 or so should be sufficient. You can also perform some internal rotations but I suggest to use a ratio of 3/1 ext-int.
What I also did was dropping all overhead movements since its the primary cause of rotator cuff wear.
I found bench pressing with sligtly narrower grip to be ok. that was sufficient for my pushing strength until my shoulder rehab was over.
I also exchanged pull ups with rows since vertical pulling, especially pull ups (abduction+external rotation) seemed to impact the rotator cuff.
Loads should not be very heavy, I stayed around the 10 rep range most of the time (quite high compared to my usual training) and only did one set to exaustion.
I found light accessory movements to be fine to keep working and strengthening my delts without stressing rotator cuff out. Particularly I found Waterberry’s and Cossgrove’s “monster shoulders in 8 weeks” first phase to be very useful for that purpose.
Remember to give time to see how your shoulders feel after every workout (the next day) and proceed accordingly.
Hope that helps, wish you a quick recovery