You will never see permanent improvements in how your body moves if you don’t also train with weights. Go with dumbbells and kettlebells as they allow you to move freely without being fixed to a barbell. Lifting weights doesn’t have to mean barbell. The body works by you improving a position and then using any changes you have made with some load and tempo. The biggest mistake people make is stopping training for a long time to just work on mobility. It will not get you where you want to go. You have to train within your current capacity.