So... is Nyanko Days finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 26, 2017
Manga finished: October 27, 2020
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Nyanko Days follows Yuuko, a shy high school student who struggles with social interactions at school.
Her real comfort and joy come from her three cats, Maa, Shi, and Ro, who are special because they can talk and have human-like forms.
The anime focuses on the daily life of Yuuko and her feline companions, showcasing the heartwarming bond they share and how the cats help her navigate her shyness and make new friends.
It's a slice-of-life story about friendship, companionship, and the joy that cats bring to Yuuko's otherwise ordinary life.