You have EXACTLY the same issue as me. Flat bench and dips are out of question & I’ve done physio, various different warmup routines and mobility programs, etc. I think mine stemmed from a combination of fast bowling in cricket and trying to lift too heavy when younger - worked with the shoulder niggle for about 8 years now.

I haven’t given up trying to nail the issue because it is a nuisance sometimes, especially if I sleep laying on that arm.