So... is Mugen no Juunin: Immortal finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 26, 2020
Manga finished: May 24, 2024
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Mugen no Juunin: Immortal follows the story of Manji, a near-immortal swordsman burdened by a bloody past.
Seeking redemption for his violent deeds, Manji makes a pact to kill a thousand evil men in exchange for the potential removal of his immortality.
His path intersects with Rin, a young woman seeking revenge for the murder of her family.
Initially hesitant, Manji agrees to protect Rin, and the two embark on a dangerous journey together.
Their travels lead them through a landscape of bloodshed and vengeance as they both strive to achieve their individual goals: Manji seeking atonement and Rin pursuing justice.