So... is Karakuri Circus finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: June 27, 2019
Manga finished: May 31, 2006
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Karakuri Circus tells the story of Masaru, a young boy who suddenly inherits a massive fortune and becomes the target of assassins. These aren't ordinary killers, but rather powerful, humanoid puppets.
Masaru's life intertwines with two unlikely protectors: Narumi, a man with a strange medical condition who can only be cured by laughter, and Shirogane, a mysterious white-haired girl who is a puppeteer herself.
Together, the three find themselves caught in an ancient conflict between humans and puppets, uncovering secrets and facing deadly threats as they try to survive and protect Masaru from those who want him dead. The story explores themes of love, betrayal, and the enduring struggle between humanity and artificial beings.