Honestly, I don’t like the look of your old form. You’ve got an excessive arch in your lower back and I’d wager you’re doing harm to your abdominal recruitment patterns (instilling an improper length/tension relationship). I used to lift the same way (very arched back, anteriorly rotated pelvis) and it showed up strongly on the track.
Your new form combines excessive (though less severely so) arching at the top and couples it with what is probably too steep of a torso angle. Your lower back should not be the primary thing getting sore from squats.
I don’t know if I’d have you squatting at this point in time. I’d probably put a lot of emphasis on hip mobility and abdominal coordination.