I've said it before, and I'll say it again: All the evidence so far at this point in the story feels like it heavily implies that Tsukasa was born a human in a Japanese capital of antiquity like Nara or Asuka (reference: one of the end-of-volume Q&A sessions and Chapter 30, where they went sight-seeing around Nara and it felt like it was very nostalgic and depressing for Tsukasa, but she was resolved to make new happy memories with her husband to replace the old, traumatic ones), and the only real connections to the Tale of the Bamboo Cutter are that the events of the tale were happening at the same time she was growing up, and the only deviation in the tale is that the elixir of immortality at the end didn't get destroyed and ended up administered to Tsukasa instead (in her 16th year of life, to explain why she's frozen at that age in every instance we've seen of her in the past), likely by a loving father that was probably one of the people tasked with the destruction of said elixir. Defying imperial decree meant his life was forfeit, which means trauma for little Tsukasa.
Any other deviation in the tale would be too big of a detail to change. She can't be Kaguya, because there's no way she would have avoided going back and staying with her people. People believing she could be Kaguya herself really were over-reaching.
Tsukasa has all but been proven to have lived on the Earth for pretty much all of the intervening thousand-plus years between when those events happened and modern-day at this point in the story, if you paid attention to all the details from chapter contents to end-of-volume Q&A's and even the splash page art from these first ten volumes.
The moon rock is quite likely something procured secretly from the American Apollo Program and is either just a remarkable souvenir of human achievement or part of research to undo Tsukasa's immortality 'curse' so she can finally live a normal human life again - this is what I believe the real end-game of this manga will actually be about. I've said before multiple times that it cannot be something that has been kept by Tsukasa since time of antiquity, because the ability to preserve it properly wouldn't have existed until the modern era, anyway, and the moment the rock is contaminated by oxygen, it can no longer be restored and preserved and keeping it like that would be pointless.
The moon focus feels like some major misdirection, to be honest, alongside that flashback showing Tokiko and Tsukasa's first meeting- everything points to the older one being Tsukasa, despite appearances in the flashback itself, and that Tokiko actually owes Tsukasa her life and was raised by her, until they became traveling buddies, most likely. Reminder that hair and accessories in it can be easily changed. Jumping to conclusions just because of a character's hair in a flashback is pretty foolish, especially when existing evidence prior to the scene doesn't support the conclusion made with that jump.
... Also, I mentioned trauma, and I feel like that helps explain why she's generally seemed so distant and stand-offish with people in general, alongside the fact that immortality takes its toll on a good person's heart. They have to watch everyone they grow close to die before them.
If something isn't done about the situation, she'll have to watch the man she loves grow old and die and she has to live on with that pain for potentially aeons to come. Fortunately, the man she loves is a brilliant academic, and one of his Q&A responses said he was an expert in biochemistry, which felt like a vital thing to note going forward.
