In general the speed of healing of joint replacement surgery, "time to happiness" for a patient is hip faster than knee faster than shoulder which is faster than elbow surgery. This also holds for joint interventions without replacement.
One of the skills of an orthopaedic surgeon (my brother likes the "fancy" spelling) is to properly set the expectation level for the patient. Most patients will regain nearly full function, for other patients, the goal of the surgery is to limit the loss of function to where the patient is now.
@tjones you are smart to have discussed with your surgeon your concerns about archery/shooting. Understanding what is expected with a general case and applying it to your specific situation can help a brain understand what is going on with the body.
Perhaps ask about coyote rifle hunting, shooting opposite shoulder? But just shooting a rifle isn't the only concern on a recently repaired joint. How often does one take an unexpected fall while moving through the woods?
After a very successful gall bladder removal, I told Mrs kansasdad that I was considering an outing to look for morels. She looked at me as if I was nuts.
"What happens if you trip and fall on your incision?"
"Good point, I probably should do stuff that reduces the risk while I'm still in healing mode".