After Columbina recives the Trilunar Authority from the imprisoned Moon and becomes the ultimate Moon Goddess, she does three crucial things as part of her plan to be reborn after her death:

1)Her body escapes the prison after her death and becomes Kuuvhaki, and by Kuuvhaki I mean ALL of it (yes, she’s the reason Kuuvhaki exists in the first place)

2)She hides her Trilunar Authority in the real Frost Moon beyond the fake sky

3)Her soul remains in the prison, anchored by Luonnotar, the soul fragment she created when traveling to the past. During Dottore’s boss fight, Luonnotar manifest itself and calls her soul from Nibelung’s prison. Luonnotar becomes Columbina’s soul itself

During Dottore’s boss fight all three “main“ parts of Columbina are present -Body (Kuuvhaki), Soul (Luonnotar), and Trilunar Authority (Frost Moon).

The Frost Moon (Trilunar Authority) is brought down by Nicole, Varka and Arlecchino, and the three pieces of Columbina “fuse” and the Columbina with full moon authority from Nibelung’s prison is reborn.
Quick Summary of Columbina’s physiology and what she did