So... is The Legend of Heroes: Sen no Kiseki - Northern War finished or not?
NO, it is not finished.
Why?
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
The anime follows Lavi Winslet, a rookie in the Northern Jaegers, a mercenary group operating in the economically struggling region of North Ambria. North Ambria faces hardship after a catastrophe involving a mysterious event that turned buildings and citizens into salt, impacting the economy badly.
Lavi and her team are assigned to investigate Erebonia's Imperial Hero, who poses a potential threat to North Ambria.
As Lavi delves deeper into the investigation, she begins to uncover the complex political landscape of the continent, hinting at hidden agendas and larger forces at play beyond what she initially understood.