So... is Koi Kaze finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: June 18, 2004
Manga finished: January 01, 2004
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Koi Kaze follows Koushirou, a wedding planner struggling with his own romantic life due to a complicated past. He's recently been dumped and is feeling adrift.
His life takes an unexpected turn when he develops feelings for a young woman.
However, he soon discovers a shocking truth about her identity, which complicates his already troubled emotions and forces him to confront his family relationships.
The anime explores themes of love, family, and the challenges of navigating complex relationships under unusual circumstances.