So... is Gleipnir finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 28, 2020
Manga finished: April 20, 2023
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
Gleipnir follows Shuuichi, a seemingly normal high schooler with a monstrous secret: he can transform into a strange creature.
His quiet life is disrupted when he rescues a girl, Claire, from a fire. Claire quickly discovers his secret and, revealing secrets of her own, forces him to work with her.
Together, they embark on a dangerous journey to uncover the truth behind the existence of monsters and find Claire's missing sister, encountering others with their own agendas along the way.