I did some amateur boxing years ago and one thing many don't appreciate is how much impact your shoulders take in heavy bag work. Schmoes throwing arm punches can flail away all day but if you have good form and hit hard and fast, all that impact is being absorbed by your arms, shoulders and body. The first guy that trained me as a teenager said for that reason he didn't even hit heavy bags anymore, just focus mitts, pad work and sparring. I've had recurring AC joint and rotator cuff injuries from years of bad form in barbell benchpress but would also periodically do a heavy bag session if my gym had one. I've since corrected my BP form by switching to suicide grip with elbows in but hadn't hit bags in a few years. Two months ago my last workout before my gym closed, no one else showed up for BJJ so I did a heavy bag session by myself. And my right shoulder was hurting for a month and a half.
Re. cycling, I've always liked it for active recovery but IMO those tiny hard plastic racing seats are a recipe for making yourself sterile. If it's causing you pain, just get one of those wide cushioned seats that are more comfortable. If it allows you to ride without pain, it's a no brainer.
Re. lifting weights, without fail the ways I've injured myself have been 1) going for 1RM and 2) cranking out crossfit style AMRAP with shitty form on last few reps because "feel the burn, bro." Fuck that, it's not worth it. Always leave one or two reps in the tank and live again to lift another day without injury.
I've trained a lot of different combat sports over the years and am lucky to still be doing it in my mid-40's, but one thing that's helped me was forced multi-year breaks in between job relocations and/or getting tied up with family stuff. In hindsight, that's been instrumental in helping me recover from nagging injuries and re-starting the combat sport again a few years later with renewed enthusiasm.