You're confusing two meaning of the word "the same." When we refer to a person as "the same" that doesn't mean they haven't changed, it means that they've changed in some ways, but not in others.

Sure, I'm aware of that. But the bit that you quoted didn't make claims about what "the same" means in any objective sense - it only said that if you choose your definition of "the same" appropriately, then you can stop worrying about your long-term survival and thus feel better. (At least that's how it worked for me: I used to worry about my long-term survival a lot more when I still found personal identity to be a meaningful concept.)