I became a CEO and feel like I’m performing leadership rather than doing it. Why?

You feel like you are performing because much of what you bring to the role is a performance. That is not an insult. It is what years of being rewarded for the acceptable version of yourself produces. By the time most people reach chief executive they are fluent in a part written by every organisation they passed through. The title gives you positional authority, which is loaned. Take away the title. What is left is your authority. If that lands somewhere uncomfortable, you have found the work.