So... is Mushikago no Cagaster finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: February 06, 2020
Manga finished: May 19, 2016
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Mushikago no Cagaster tells a post-apocalyptic story set in 2125, thirty years after a strange disease called "Cagaster" began transforming humans into monstrous insects.
The narrative centers around a young insect fighter named Kidou.
The anime explores his journey in this insect-infested world, suggesting a focus on survival and perhaps uncovering the mysteries surrounding the Cagaster disease itself.