From what I understand chakra is not only a power system but it's also your soul and mind, after Kaguya was sealed, her soul and mind were ripped apart and molded back into the tailed beast, each with their own individual soul and mind, the thing left in that dimension was a empty husk(the gedo Statue)

Hell zetsu even said that he was reviving Kaguya, why do people think that kaguya had this Zamasu/Aizen levels of immortality, from what I see Kaguya just has her basic Otsutsuki immortality where they won't die of natural causes but they can die by external forces and her high Juubi Regen that still can be killable as we see Madara saying that he almost got killed by guy(yes he let himself get hit but he still admitted that he almost died by it)