I mean, she's technically not even human anymore, right? A Hōrai immortal might as well be a different yōkai – which does open the possibility that it is human belief and primal yearning for not-dying that keeps the Hōrai effect going. So if humanity is wiped out, Kaguya, Eirin, and Mokō will pretty much disappear along with the other yōkai.
Sure Eirin herself might predate humanity, but there's also the angle of human belief retroactively creating the history. 🤔 Like the birth of Slaanesh in Warhammer 40000 making it so that she has always existed.
