So... is Izumo finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 21, 1991
Manga finished: July 26, 1993
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
Izumo follows the journey of a young prince named Izumo in a mythical ancient Japan. Dissatisfied with his life, he dreams of adventure beyond his kingdom.
His world is turned upside down with the arrival of Sanae, a mysterious girl with ties to a secretive group with magical abilities, who becomes entangled in a dangerous plot.
When Sanae is kidnapped, Izumo is forced to embrace his destiny. He must learn to wield a powerful, legendary sword to save her.
His quest is complicated by the resurgence of an ancient, terrifying monster, the Yamata-no-Orochi, which he must overcome before he can hope to rescue Sanae and protect his kingdom.
With the help of an unexpected ally, Izumo embarks on a perilous adventure, facing powerful enemies and uncovering secrets that will challenge everything he thought he knew.