i don't really think that she is necessarily die, I think the swan dream symbolize that while she did suffer when the parasite died, she is finally able to accept life without the parasite "But as she swam in the lake upon which cherry petals fell, things gradually stopped mattering. Well, in the end, at least I'm able to have this beautiful sight all to myself, thought the swan." and idk about japan but swan also symbolize stability. but again, it was just a dream and we all know what was in Sanagi head before that dream