I've had it for about 10 years, caused by gradual damage from upright rows. It was my first long-term injury and I was very ignorant about MSK at the time and actually had it for 3 years before I realised, since I thought the pain was normal muscle weakness (even though I could barely hold a phone up in the normal way for more than 10 seconds lol), until I badly tweaked one shoulder in judo and afterwards realised the other one basically felt the same and they both must've been injured.
Physiotherapist's simple band exercises (thumb-up lateral raises and banded rows) and being mindful of getting my shoulders more down/back (relative to my norm at the time) fixed it 70-80% within a couple months, near-daily doing light high-rep shoulder exercise like cleaning windows with a towel and vacuuming (was part of my job at the time) while trying to keep my scapulae neutral to build stability helped too, plus full pullups. Kevin Lee mentioned hanging on a bar with a thumbless overhand grip helped his shoulders feel better, so I do that sometimes. I casually did exercises for it regularly for several years trying to fully fix it, not done it for a couple years now though. I'll still feel a light pain very occasionally and it's likely to flare up if doing any horizontal pushing exercises or boxing (which I don't do often). On the other hand, I find doing pushups can help, if I focus on keeping the scapulae stable and let that be the limiting factor, to build strength in the stabilising muscles.
If I understood your rear delt description correctly, it seems your tendon hurts when your shoulder comes forwards and horizontally adducts more. Maybe that's quite common with rotator cuff issues or at least I'm pretty sure it happens to me too. I know when the scapulae protract and during horizontal adduction it reduces the subacromial space (in different ways) and tendons can be pinched between the humeral head and another bone or ligament, so maybe that's happening. From what I've read, scapular dyskinesis, posture, and weakness of the rotator cuff muscles themselves (since they stabilise the humeral head) can all play a role. I'd ask a PT about that rear delt phenomenon - maybe it is a case of avoiding that motion, unless there is a way to strengthen something or adjust posture to stop it hurting.