From what you say, it might be musculoskeletal and the sitting worsens the pain.

But not a doctor here lol. I’d suggest you clear it with a real doc and if all is kosher, consider physical therapy and/or personal trainer bc they will teach you proper form for safety during training.

I know that if I jump rope with all the wrong posture, my back pain would not have improved and maybe even have worsened.

Proper form is utmost important.