So... is Hitsuji no Uta finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: February 25, 2004
Manga finished: September 30, 2002
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Hitsuji no Uta tells the story of Kazuna, a young man who was separated from his family as a child and raised by foster parents.
As he enters his adolescence, Kazuna begins to experience strange symptoms that hint at a dark family secret: a hereditary illness causing an intense craving for blood.
He is reunited with his older sister, Chizuna, who has lived with this condition for many years. She attempts to guide him through the challenges of managing his newfound desires and the heavy burden of this inherited affliction.
The anime explores Kazuna's struggle to come to terms with his identity and the implications of his family's past while trying to maintain his humanity.