I share your skepticism about Butler’s claims about gender being performative, though I understand the basic direction she is going with it. From reading the rest of her writings, I think that Butler places too much emphasis on cultural determination of personal identity and this creates problems for her across her philosophy. So when she tries to include personal autonomy, she has no place for it within her philosophy, and it rings hollow like the point on which you are commenting. You astutely point out that her view calls into question how a gender performance could be inauthentic or hidden under a false performance.

You bring up an interesting question: do we experience gender, and if so, what is it that we are experiencing? Are there internal and external components of gender that we can experience? Some people say they “feel” like a woman or a man. How is that? What is that? Is that expression of feeling a performance of gender? We need to listen to such expressions and try to understand.