So... is Umi no Yami, Tsuki no Kage finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 14, 1989
Manga finished: October 26, 1991
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Umi no Yami, Tsuki no Kage centers around twin sisters, Ruka and Rumi, both vying for the affection of the same older student, Katsuyuki.
Initially, the relationship seems like a straightforward love triangle, with Rumi appearing supportive of her sister's pursuit.
However, everything changes when a mysterious bacterium infects the twins, granting them powerful psychic abilities and drastically altering Rumi's personality.
Rumi's obsession with Katsuyuki intensifies, and she becomes willing to do anything to win his heart, creating a dangerous conflict between the sisters and threatening those around them.