Personality does matter a lot in leadership.
But I believe one does not have to choose between the two. You can be an introvert AND an extrovert.
I was an introvert. I rarely go out with friends. My parents forbid my siblings from going out while I was encouraged to. Yet going into entrepreneurship made me realize how important it is to really connect with people. So I started learning how to be more sociable. I look people in the eye, shake their hands firmly, and open up conversation.
It’s not impossible, you just need to be willing.