thinking of grace as the muse and the process of eventually regaining past memories and how complicated and messy that is. to some extent it's manageable, if weird. i think the more distant things, past lives from ages ago, would be distant enough it's manageable, depending on the experience. there is, of course, the fact a lot of the experiences are not things she experienced and a lot of them would be really bad, traumatic events.
they say in game you feel as if you lived those things yourself, so it wouldn't be like remembering something someone else lived; it's reliving that trauma as if it happened to her. even the milder, if they can be called that, but like... life stuff like marriages and children; she never experienced those things, but it would feel like she had. it'd be confusing, to say the least, as she tries to adjust to it and to what she is in the middle of all that; but i think it gets far worse when it comes to experiences and feelings related to people she's close to.
calliope and apollo, for example, are shown to be close throughout ages. whether they were friends or like family or if it had romantic undertones, it doesn't matter; what matters is grace has her own feelings about him, but then there are other feelings that come from calliope and all the previous incarnations and things they lived that feel like grace lived them, good and bad. how do you separate what's you and what came before? how does that influence things? how does it change things?
the same goes for persephone, and with her we have a better defined relationship with calliope. they were romantically involved. they fought badly. it'd feel to her as if she had been in love with persephone — and as if she had been the one often clashing with her too. it's impossible that for a time, especially when first regaining these memories, they wouldn't mess with her. how do you not let it change how you feel when the previous experiences feel like they're yours?
given how grace is as a character (driven, headstrong, with a good sense of who she is despite feeling... adrift) and the fact we hear in game some incarnations are able to retain their current personalities rather well, keep their names and everything, i like to think that would be the case with her. i don't expect, even in the long term, she'd want to be called calliope (the idea seems wild to her initially, but after regaining the memories i feel she'd understand better why others would do it, even if it wouldn't be her choice); and i think it's obvious the memories and feelings would change her to some extent, because we're all shaped by our experiences and those feel like her experiences, but i also think past the initial confusion (which would be great and messy) she'd be able to continue being herself.
during the process though i'm certain things would get confusing and more volatile, no matter how careful and mindful of everything she tries to be. there would be terrible days; tears that are hers but aren't, anger that is hers but isn't, fears that are hers but aren't. feelings for those closest to her she isn't sure are hers or some past calliope's. knowing what it's like to kill, or give birth to a child, or lose a wife, knowing great joy and great sorrow from things that would've seemed so distant from her reality before. it's a little insane; it'd make her feel a little insane. having support certainly makes a huge difference, but ultimately a lot of it is in her head and she has to go through it alone.
i think it's also after that that she'd have a better concept of like, immortality. because although she is immortal, she's in her 20s — she can't conceptualize what eternity looks like. but having lived through all those lives, in a way... that changes things. she'd get it better. she'd get some other things better, about what she became and her powers and what's that all like, as well as about some of the other gods and how they were and what they've been through. she knows some things, but living them (or feeling like she did) is something else.
but yeah, ultimately while it's all part of who she is and what she became, i don't think they'd define her. in a way, the adrift reprise where she's the muse is aligned with this, i feel. it's finding herself through these other lives, too, that are invariably part of who she is, but do not make the whole and don't change the core.