So... is Nejimaki Seirei Senki: Tenkyou no Alderamin finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: October 01, 2016
Manga finished: August 10, 2018
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Nejimaki Seirei Senki: Tenkyou no Alderamin follows Ikta Solork, a lazy and womanizing young man whose idyllic life is interrupted by war. Forced into military service alongside his childhood friend, Yatorishino, Ikta unexpectedly becomes involved in a crucial rescue mission.
He and his new comrades, Matthew, Torway, and Haroma, find themselves stranded in enemy territory and tasked with saving Princess Chamille, the imperial heir.
Their success unexpectedly thrusts them into positions of power and responsibility, specifically as Imperial Knights. Ikta is forced to abandon his dream of a peaceful life and confront the realities of war and political intrigue within the Katjvarna Empire.
The story will explore how Ikta, despite his initial reluctance, navigates his new role and contributes to the ongoing conflict, changing both himself and the world around him.