Anyone knows what variable is responsible for this? Can't find a proper ID in CS game settings.

I see fEnchantmentChanceMult in the gmst list. The formula for successful enchanting and successful recharging might be using the same multiplier, just a different formula. I'm just not seeing anything else on the list that would pertain to soul gem recharging. You could try changing this number to see if it increases the chance to recharge an item, but it will also affect the success rate of creating a new enchant too I'm guessing.

Did that. Lowering this ID from 3 to 0,03 increased Enchanting success to >100% on skill=10. With Recharging - no difference: on skill=10 it stays the same.

I have no idea how to find what your looking for but increasing intelligence seems to increase recharge more then the success of creating an item. They seem to be linked to each other for the most part but that was the bigger difference. I also know lower soul gems succeed a lot more then better ones. Try Magic item recharge whatever since that is the only real thing that indicates anything about recharging. If you could find the script for the soul gems it might be more useful. I was in-able to find it however.