What are unique ways to write immortal characters?

There are two immortals in the book I'm writing, Rose and Azalea

Rose took it badly. She fell in love with a mortal, and when he died she went into a spiraling depression which she never really recovered. She drove herself insane either trying to bring him back to life (which is impossible) or to kill herself (which is also impossible). She was so fixated on what she'd lost that she never really considered the life ahead of her.

Azalea on the other hand is an expert at forcing herself to forget things. She lives in a place for a certain amount of time, living a perfectly normal mortal life, and whenever she's bored of it, or her partner dies, or she loses a job, or really any other reason, she packs up, goes somewhere else, and forces herself to forget her past life (which she can do because magic, and even without magic, she has a normal human memory). She keeps popping up in different stories i'm writing with a completely different personality because she keeps reinventing herself. To her, she is a different person, because she barely remembers who she was a few decades ago

/r/writing Thread