firts I think, you should give the other single kick side a try and analyze.
Without having seen you I'd guess it's more a matter of tiny alignment difference, curved spine or hip legs connection
To find out: What happens, with strong and long push off and SG to skate earliest on both sides without any kick?
What happens, if you extend your stroke extremely 3/4 skate position and 1/4 other stroke parts right/left? (Even breathing might help.)
What happens, if you swim with only one arm other tucked. Breathing on right side one lap and breathing on left side same arm next lap... And with other side?
What happens, when swimming kickless like with an ankle band. Whole legs still... tight at knees... "rubbing" feet while kicking just from one side toes to other side heel and vice versa.
Will you find any further asymmetries that might be the first reason?
As ever, all FWIW, wish you an exciting investigation with best results and with..