So... is Bungou to Alchemist: Shinpan no Haguruma 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
Bungou to Alchemist: Shinpan no Haguruma tells the story of famous literary figures resurrected by a mysterious Alchemist.
These reincarnated authors are bound to a massive library and tasked with a vital mission: to dive into classic books and eradicate monstrous Taints that are corrupting the narratives.
Their goal is twofold: purify the tainted texts and rescue other trapped writers, adding them to their ranks.
While some authors retain echoes of their former selves, others struggle with amnesia, their memories of their past lives and literary works fragmented.
Driven by a hope of unraveling the mystery behind their rebirth and addressing unresolved questions from their past, these literary heroes embark on a seemingly endless battle to preserve the integrity of literature itself.