The anime only covered volumes 1-3 of the LN. The story still continues in volumes 4 and 5; the anime also left out some details which foreshadowed the events of those two volumes.
I'm not sure how far the manga will cover, but it's very possible that it will include the full LN story.
As for "a sequel series focused on another set of characters", that would be SukaMoka, which focuses more on the next generation (Collon, Lakhesh, Pannibal, Tiat)
On another note, it's interesting to see the art style of this manga - it's quite distinct from the LN and anime