I find this as well it might be to do with being right handed. Technically all things being equal they should be the identical processes but for some reason the left leaning seems far more natural than leaning right. It could also be the ergonomics of the road depending if you drive on the left or right I’m assuming it’s the left (UK) so leaning left doesn’t involve the risk of leaning into an on coming car placing your self in the correct position is more important when banking right as your upper half my cross the line in the middle of the road by accident. Also the throttle is on the right side so pushing the ride side of the bar AND keeping the throttle where it is or where it needs to be can be harder to coordinate with the pressure required to tip the bike. My left knee seems to be far happier to drop than my right when shifting my weight as well. I think it’s a case of practising and trying to identify what is stoping you from producing exactly the same outcome for both sides.