You’ve got all in info, let’s put it together.
You’ve got the sore hip. Torn cartilage/labrum shows your “femur ball” is in the wrong spot. Artrophy in your hip joint shows you the under-active tissue that isn’t working to hold your “femur ball” in place.
Your hip isn’t working properly, so when you do big moves other stuff has to make up for the lack of hip motion. That’s why you’re beat up after squats/deads. And in good alignment when you don’t do those lifts.
If you can “wake up” those atrophied muscles, or rehab that hip joint, or restore your hip function your hip will be stable and move better. Then big moves won’t mess you up so bad.
But you have to get that hip joint working again! And until then you can only do lifts that “fit” into the range of motion your hip has now. You have to stop messing yourself up and making it worse until you get your hip joint right. You have to figure out how to control it and make it work.
If you start only doing what doesn’t hurt and ignore the joint motion, you’ll keep losing hip ROM. More and more lifts will hurt until you’ve got none left! This path ends in a hip replacement.
But you can head that off with some focus on hip tilts and Glute activation.