I feel like people are ignoring the symbolism here. For Sachiko, the moon is eternal, a sign of the bright love she shares with Mizuki even as they're far apart. For Mizuki, the moon is ephemeral, a far away symbol of her girlfriend who continuously shifts further away from her as she becomes more and more famous, and in the end, its ephemerality for Mizuki naturally turns into ephemerality for Sachiko, and the symbol breaks in half when the contradiction becomes apparent. I can't say for sure what Mizuki was thinking (part of the point of the story is that we don't know), but the fact that she stuck with Sachiko for two and a half years while she was in Tokyo before her debut suggests that she did in fact view the relationship seriously.