Character class should weight on the skill power

So, here comes the battle update. Everything (apart some bugs) seems good and fine (also exciting for new strategies and way to battle)

The only thing that i feel is a bit off is that (for example) warrior can heal, or do other skill that were just a unique skill of other class. Feel just a bit weird, mage skill being used by archer and rogue one by healer.

The idea i came up with to try to fix this, is to provide some sort of "class powerup" or a separate base stat that, for example, improve the dmg/stats or the cooldown of some skill

So healer should start with a 3 turn cooldown on healing, rogue with lower cooldown on gambit, archer with higher dmg on soul shot (headshot?), mage should have more dmg absorbed with arcane barrier
Something like "special attack" or "class skill stat" that improved only some skill tree