So... is Heike Monogatari finished or not?
YES, it is finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Heike Monogatari tells the story of the powerful Taira clan and their impending downfall. A young girl named Biwa, who possesses the ability to see the future, is taken in by Taira no Shigemori, a member of the clan. Shigemori is troubled by the clan's actions and seeks to prevent its prophesied demise. The anime explores the political tensions, the burgeoning war, and the relationship between Shigemori and Biwa, as they navigate a pivotal era in Japanese history. Biwa's knowledge of the future and Shigemori's ability to see spirits add layers of complexity to their efforts to understand and potentially alter the clan's fate.