While she is most certainly some version of Kaguya-hime, this is obviously a very different story from the original.
For one, she got married in this one, was adopted at a much older age than the original, the moon rock, etc.
If I had to guess, assuming this story reaches the end without getting canceled, rather than being taken back to the moon by the other moon people, the series slogan “fly me to the moon” will become literal, and Nasa-kun will eventually have to help her get back to the moon, either by building a spaceship, or by getting her a ride on some existing ship headed to the moon.
But honestly considering that this is the first hint of the plot returning in like 30 chapters or longer, well, I tend to doubt the story will ever reach that point.