My guess is that she wished something like:
”I wish that when I meet him again, he will only see the things he like in me, and nothing else”
and thus the charm split her, and asked him to make a choice, making the part of her personality he wouldn’t like disappear.
And I guess that in the end, he’ll prove that he love every facets of her, and she will fuse back into a single full person, or something. There was an old manga a long time ago (a decade?) that had a VERY similar premise… It’s way too early to judge if this mangaka is able to write it as well and that past one, or if they will differentiate it later… (it have been mentioned a couple time in this thread)