N+1 Hip labral tear here…4 years ago was in constant pain, could barely ride my bike and was told I needed surgery by sports dr, physiotherapist and of course orthopaedic surgeon…however, I finally opted to try eliminating muscle tension I had, improve function and strengthen the hip…all pain went within a few months and never went back to the surgeon. I have a martial arts friend who took a similar approach to fix his shoulder.
Of course every case must be treated on its own merits and perhaps your shoulder is much worse but I would certainly look at PT/non invasive treatment first, if nothing else it will serve as good pre-hab before an op and accelerate recovery
Good luck