So... is Seirei no Moribito finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 29, 2007
Manga finished: December 13, 2017
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
A kingdom faces a potential environmental disaster, and ancient prophecies suggest a way to avert it: the sacrifice of a water demon.
Unexpectedly, the water demon appears within the emperor's son, Prince Chagum, leading to a decree for his execution.
However, Chagum's mother secretly enlists the aid of Balsa, a skilled spearwoman, to safeguard her son from his own father's machinations.
Balsa, bound by a previous commitment, accepts the perilous mission of protecting the prince, embarking on a journey filled with danger and the promise of unforeseen connections.