The question boils down to: Is being a girl/woman today, where you live, so bad that it takes more than 99 million dollars to make up for it?
Honestly with a million dollars you could just become a cis-passing trans girl and still have at least $800,000 left to spend, if not >$950,000. Or in other words, the button gives you a 1% chance of only you becoming a girl, versus a 99% chance of you and at least four others becoming girls, assuming that you spend the remainder of your wealth on funding other girls' transitions. Though you could just as well spend that money on funding trans advocacy and medical research or other sorts of long-term investment.
From that perspective, the 1% chance seems like a loss. What does "become a girl" even mean? Are you transported into the timeline where you were AFAB? Are you transported into the timeline where you had a botched circumcision and your parents decided to raise you as a girl despite being told not to? Is your body just magically poofed into a cisfeminine phenotype? Is this the timeline where you transitioned MTF but did so before puberty? Is this just the same as transitioning MTF but now the folks who won the million dollars are sponsoring your transition? Is this the same as transitioning MTF but all of society has with a snap of the fingers unlearned all transphobia, getting rid of the social and material barriers to transitioning?
There are so many questions one can ask about this premise, like, "What would it mean for me to have been AFAB? Same zygote but with a random AR mutation? Do I keep my old memories from when I was a boy?", or, "If I was circumcised, and have my genitals magically transformed, have my new genitals undergone type 1a FGM? What happens to my secondary sex characteristics?", or, "If I'm magically transformed, is my ID also magically changed? Does God drop down some boxes of tampons and new clothes from the heavens above?".
I would ask the maker of the button to write some very clear terms of service, because this seems like it could be a real monkey's paw...