I have been through it. I am sure every case is different, so my story may be very different from how yours goes. I had adhesive capsulitis, bursitis, involved bicep tendon, and partial rotator tear. The surgery included removal of bursa, acromion ground down, capsular release (shredded interior cleaned out), and bicep tendonesis. Rotator cuff was not repaired. They felt it was minor enough to respond to post surgical rehab.
For me, the biggest thing was having to learn how to to hold myself back from pushing too hard too fast. Having been through tremendous pain for around a year prior to surgery, my pain threshold was very high, and I am not so sure that the doctor really understood how much pain he was recommending pushing through or whether he really knew climbing. So, I had to learn from my own longer term rehab experience. And I did push myself too hard and suffer from it.
Very frustrating, but it took a very long time. Every time I pushed too hard, it would flare. Every time I backed off, it would improve. One guide after around 8 weeks of rehab was, if I did anything that made me feel like I needed to ice it, i was doing too much.
I think finding your own tolerable level of "soreness" is good semantics, but if you start calling it "pain" you might be going too far.
The main thing through it all was working to keep the joint mobile, striving for full range movement while avoiding impinging. However had to learn to do so without setting it off again.
In terms of the pain vs soreness and how hard to push, the right PT can guide you. Over the course of the injury, surgery and rehab more than ten PTs worked on me. There are some i won't let touch me again. There are some that are gold. I learned it pays to shop around.
It was 6 months after surgery that I could do my first pull up and started to climb again. Then around two years until it started to feel pretty normal. Then a minor relapse for another year, though I believe it was from a prescription drug "side effect" which caused multiple tendonitisis in various joint areas, along with muscle wasting.
Now, 4-5 years post surgery, I need to keep up the stretchy band routine or it acts up, but it generally feels normal, and push ups and pull ups within reason help. Divebombers are still really hard to not impinge. But, I am no longer constantly afraid of re-injury, overhang climbing etc.
So, at least in my case, it took a lot longer than I wished for, and it taught me a new level of patience, but the shoulder works and is mostly pain free.