So... is Outbreak Company finished or not?
NO, it is not finished.
Why?
We found unfinished non-core content:
Paramilitary Company: Moeru Shinryakusha (Other)
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
Outbreak Company follows Shinichi Kanou, a reclusive otaku with encyclopedic knowledge of Japanese pop culture, who unexpectedly finds himself transported to a fantasy world called the Eldant Empire.
Tasked by the Japanese government, Shinichi must become an "Otaku Missionary," introducing anime, manga, and video games to the people of this medieval-like realm.
With the assistance of a half-elf maid, Myucel, and the young Princess Petralka, Shinichi faces the challenges of navigating cultural differences, political intrigue, and social prejudices as he attempts to spread otaku culture in this new and unfamiliar land. He must use his knowledge and passion to bridge the gap between his world and theirs.