Even assuming this argument is correct, Sleeping Beauty doesn’t know everything exactly when she wakes up, and it won’t be the same. For example, she has a 50% chance of waking up facing right if she wakes up once, but a 75% chance if she wakes up twice. If you include everything she experiences, she’s pretty much exactly twice as likely to get that experience if she wakes up twice.
Even assuming this argument is correct, Sleeping Beauty doesn’t know everything exactly when she wakes up, and it won’t be the same. For example, she has a 50% chance of waking up facing right if she wakes up once, but a 75% chance if she wakes up twice. If you include everything she experiences, she’s pretty much exactly twice as likely to get that experience if she wakes up twice.