So... is Koroshi Ai finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 31, 2022
Manga finished: January 14, 2023
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Koroshi Ai follows Chateau Dankworth, a bounty hunter, whose life is turned upside down when she crosses paths with Song Ryang-ha, a highly skilled assassin who develops an unusual interest in her.
Initially resistant, Chateau finds herself reluctantly working with Ryang-ha, who offers her valuable information on her targets in exchange for her time.
As they navigate dangerous missions and their professional relationship deepens, secrets from their pasts begin to surface, threatening their arrangement and putting both of them in considerable danger.