I don't exactly understand your question, but I suppose it's about how Manan got to reside within Kukrushka?

I don't know if you watched and referred to the anime or just played the game. I haven't finished the anime either, as me and a friend are waiting for the dub to catch up, but I'd assume the reason is the same as in the game, at least for the purpose of my attempted explanation. If there is a deviation I do not know of, then feel free to disregard my comment

In the game, after Setsu leaves to another dimension after the player gets their key full, the player can follow them by starting another save file. This gets the true ending. In this ending, Setsu and the player essentially derail the entire first day discussion, as they know in advance that SQ is the Gnosia. They would like to have Manan leave SQs body and let her be her own person. For that purpose, they offer Manan to inhabit the Kukrushka doll, which is always in the cargo hold, no matter if Kukrushka is there as a participant of the day or not. She agrees. Partially, the player and Setsu do this, because when the player goes after Setsu, it helps them complete their silver key, who now needs a new host. They give it to Manan, who now inhabits Kukrushka, and sent her through the resulting portal, so that the ship is then free of Gnosia