@Rialtoir
I think it's indeed a valid theory that reincarnation in this manga works in a way that the soul occupies a newborn body until it's finished with its business in the world.
Miya's business is finished, so her soul is released (possibly reborn as a new cat) and only the "true" Sakuya remains. Should Sakuya come into the situation that she dies with lingering ties herself one day, the cycle would begin anew.
As much as Hinata is a granny (Toyo) at heart, she's still very childlike, characteristics of the "true" Hinata.