Idk who needs to hear this but Columbinaโs story was never just about finding a family, it was about finding out if โfamilyโ was ever something she could have to begin with
She was born into the Frostmoon Scions and without choice they treated her as a god. Physically it should be her home, but she was never able to create genuine bonds that made her feel like she belonged there, and any relationship she could make would not end as mutuals
Then the Fatui initially looked like the opposite. For perhaps the first time, she was surrounded by people who treated her as a person and not Kuutar. Arlecchino tried befriending her and she slowly opened up to the girls and presumably to the others until Dottore took advantage of that.
He regarded her as his own sister, something Bina probably liked to believe as it made sense for a family, only for her to realize it was not much different from how the Scions treated her the closer they got. He corrupted one of the first relationships she allowed herself to believe in which made her doubt her previous ones (remember sheโs still socially naive)
Then the Tsaritsa led her to believe all her relationships there were a facade on some level so they can use her powers for the organization. From Columbinaโs perspective it confirmed her worst suspicions
โNobody actually loves me for me.โ
โThey love what I am.โ
โThey love what I can do for them.โ
Thatโs when she suddenly left, believing the time she had love there was merely transactional and with no where else to go and call home she wants to return to the moon. Her entire character arc revolves around regaining that trust and learning that not all her bonds were fake; there are people that just loved her as Columbina