So... is Kurozuka finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: December 23, 2008
Manga finished: October 18, 2006
... But 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
Kurou, a 12th-century swordsman, flees with his servant into a forest and encounters Kuromitsu, a captivating woman who dwells in solitude.
Their initial refuge soon reveals a dark secret: Kuromitsu is an immortal vampire. Kurou becomes devoted to her, choosing immortality himself to remain by her side.
Tragedy strikes when Kurou is betrayed and seemingly killed.
He awakens centuries later in a devastated future Japan, his memories fragmented. Driven by love and vengeance, he embarks on a journey to find Kuromitsu and confront those who wronged him.