Can't say at this point.....for me Kishi has completely changed his style of writing. To me it seems he has went from a deep, concerned, and personal writer...a writer who writes from within. To a more impromptu, make it up as I go, do whatever the fans like writer..... Imho of course.... some may see differently.
So at this point I stopped trying to understand Kishi..... I expect anything.... XD Any, and everything is possible nao to me.....
Just as Indra and ashuras chakra cling on to sasuke and naruto, maybe Kaguyas clung on to or returned back to the holy tree since the tree is the very reason chakra exists. What if hers is soo strong that it attained or retained its own personality. Just like Indra and ashura