Starting BJJ with a lot of pre-existing injuries?

I’m into my 30s with a sedentary job (in front of the computer, and remote at that). I used to be very active through college with sports, weights, running, and just overall being a young kid. Totally an excuse, but the job and life led me to become completely inactive and I’ve lost practically all muscle since then and gained like 10-20 pounds in fat.

I’ve been injured quite a few times with weights (rotator cuff, wrist, lower back) and sports (knees and ankles). The previous injuries compounded with a sedentary lifestyle has made my body feel like I’m middle aged.

All that being said, I’ve committed to getting back in shape, and my longtime interest in combat sports has led me to want to get into BJJ for all of the benefits. I’ve already been running and getting my cardio back up for the past couple of months. I’m just wondering if starting BJJ at this age and with so many preexisting injuries is even a good idea. Maybe after getting my body more back into shape? My joints already feel like they have arthritis (I don’t think they actually do, it just feels like it) because I’ve been so inactive for nearly a decade, so I’m just worried the inevitable injuries with BJJ will just make everything worse.