I think it's rare that a BPH procedure causes long-term incontinence, but not impossible. Did you have a laser or the old-style "roto-rooter" procedure?
I had a laser procedure in 2017 to remove some calcium stones that had developed in my prostate (after having had a prior TURP for BPH and then radiation treatment for prostate cancer), and for some reason the surgeon removed some tissue in my INTERNAL sphincter, which left me permanently incontinent. For over a year I was using 1-2 pullups a day.
I found a new urologist who got me plugged into a great pelvic-floor therapist. I learned how to do "correct" Kegels which has helped me better incorporate my EXTERNAL sphincter to offset my deficient INTERNAL sphincter. I also take a regiment of medications (Myrbetriq, Alfuzosin and Finasteride) which together help eliminate undue spasms and correspondingly reduce stress on my urological system.
I am now down to 1 or maybe 2 medium pads per day. This is manageable for now. I am hoping that stem cell therapies will advance to a point where I could get an injection into my internal sphincter and grow new muscle.
I would recommend finding a good urologist who will hone in on what is causing your incontinence, and what are the most appropriate therapies & treatments to consider. At this point, with my situation being as manageable as it is, I would not consider any surgical options, but if I was still using 1-2 pullups a day I probably would consider an artificial sphincter or sling.
Good luck!