If you want to model your character on Wolverine, there is definitely a way drugs could help Wolverine.
Wolverine is depressed.
This is not my own insight. His own internal torture is an integral part of the character. https://themighty.com/2017/05/logan-mental-illness/
So too your character. He is violent by nature and is plagued by rage and impulses to more violence. He is lonely and isolated, both by his own bad choices and his immortality and the fact that violence surrounds him and takes the people he cares about.
Your character rides in an awesome performance sports car - his own body. But he is not always the best driver. He could get a lot more done, and done more effectively and less painfully if he were not so depressed.
His performance enhancing drug is the fictional anti depression drug of your choice. Because of it, his sleep is more restful. His rage is easier for him to harness and control. His interactions with others feel better to him. Sometimes he can even laugh. He is more at peace, and more focused - and because of that, more dangerous to those who really are his enemies.