So... is Takt Op. Destiny finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
In a world plagued by monsters called D2s who are repulsed by music, the United States is in disarray. Music is forbidden to prevent attracting these creatures. The only defense against them are Musicarts, young women embodying classical music, and Conductors, who control them.
Takt, a talented pianist, unexpectedly becomes a Conductor and forms a pact with a Musicart named Destiny after a tragic event. Along with Anna, they begin a journey to New York City, hoping to find a way to stabilize their partnership and learn more about the Musicarts.
Driven by his desire to play the piano again, Takt is eager to reach New York, while Destiny's sense of responsibility often leads them into dangerous situations. Their journey is fraught with peril as they navigate a D2-infested landscape and face numerous challenges along the way.