I don’t know for sure, this is just my thoughts, the last series was so badly written overall, it was hard to tell.
I think the idea was meant to be that Carolyn was never really aligned with anyone else, she only cared about herself. I don’t think she was ever really part of the 12, she was just there undercover when they were formed.
I think Villanelle murdering the 12 was all her own choice, it just worked out well for Carolyn too.
By the end, Carolyn was back in MI6 and ordered the hit on Villanelle just to prove she was loyal to them.
But if anyone else saw it a different way, I’d be interested to see what you think!