I think it's pretty cute, but also probably unintended, that Tsukasa sounds a bit like "su casa", or their/your (of respect) house. It's kind of like saying that wherever you are, being with her is like you're at home.
She wants to be Kaguyahime? Interesting, I thought she was Kaguyahime, or maybe the version recorded in history aren’t quite correct and she want to be more like those.
Kaguya-hime and Space Pilot. Kaguya-hime back to the moon at the end, right? I think that means she also want to go back there and kinda envying the Kaguya-hime in the story.
Far as I’m aware, the tale is accurate. She is not Kaguya-hime. To be honest, I’m not entirely sure why she wants to be her- her characterization felt like she always just wanted to live a normal life, and being Kaguya would not be normal.
She just wants to be a space pilot because she’s fascinated by space, technology, civilization’s achievements, etc… she has no actual connection to space herself. The moon rock is really just a rock. It has no supernatural connection to Tsukasa, she just wanted it as evidence of human achievement, as a human proud of her species and excited by what we have achieved during her unnaturally long life. If I recall correctly, it ends up contaminated under Tokiko’s watch later, while she notes that it is really just some rock from space. It doesn’t matter anymore because Tsukasa found something (someone) more important to her than some rock from space.
For reference, this is all based on my knowledge from watching the anime, including the ‘High School Days’ four-part finale. I don’t know the specifics beyond those events depicted. But I have a very good understanding of Tsukasa’s character just from that. And the knowledge that Kaguya-hime is a separate character from her.