So... is Nil Admirari no Tenbin finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 24, 2018
Manga finished: June 18, 2019
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Nil Admirari no Tenbin is set in an alternate Taishou era where the era continues beyond its historical endpoint. A young woman is pressured into an arranged marriage to save her family.
Tragedy strikes when her younger brother dies mysteriously while holding a strange book.
Following this event, she discovers she can see "Auras" emanating from certain books, revealing the emotions they hold.
She's then approached by a group called "Fukurou" who investigate dangerous books known as "Maremono."
Drawn into their world, she must navigate a web of intrigue, betrayal, and complex emotions within the imperial capital, and faces a crucial decision that could change everything.