So... is Taishou Otome Otogibanashi finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: December 25, 2021
Manga finished: May 12, 2020
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Tamahiko Shima, a young man disillusioned with life after a tragic accident, is exiled to the countryside by his family. He expects to live out his days in isolation and despair.
His solitary existence is unexpectedly disrupted when Yuzuki Tachibana, a cheerful and compassionate young girl, arrives, claiming to be his bride.
Yuzuki was sent to him to assist with his daily life, but her arrival brings a much-needed ray of hope and kindness to Tamahiko's bleak world.
The anime follows the development of their relationship as Tamahiko grapples with his pessimism and Yuzuki tries to bring him out of his shell, exploring themes of healing, family, and finding happiness in unexpected places during the Taisho era.