So... is Kasei Yakyoku finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Kasei Yakyoku is set in 1923 Tokyo, a city caught between tradition and modernity. A wealthy woman becomes intrigued by a charismatic young man named Taka, who seems connected to the city's criminal underworld. Her maid, Sara, also finds herself drawn to him, creating a tense love triangle. The story explores themes of class, honor, and forbidden love against the backdrop of a city on the brink of a major catastrophe. As the narrative progresses, the looming threat of a devastating natural disaster casts a shadow over the characters' intertwined fates, promising a tragic climax.