So... is Teito Monogatari finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: September 25, 1992
Manga finished: January 01, 1990
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Tokyo, the greatest city on Earth, is under threat. A malevolent sorcerer seeks to destroy it by any means necessary.
His plan involves awakening a powerful and destructive ancient spirit linked to the city's history: Taira no Masakado.
As the sorcerer's dark magic takes hold, a diverse group of individuals, including occult experts, gifted children, and brilliant scientists, find themselves caught in a desperate battle to save Tokyo.
The struggle unfolds over many years, highlighting the enduring impact of the sorcerer's evil plot and the sacrifices made to protect the city from utter devastation.