Unfortunately the Twilight’s Hammer were mentioning Death as a gift so they were definitely working for the Dreadlords’ goals: The Hour of Twilight.
The Jailer wants the Hour of Twilight and through the Dreadlords’ infiltration of the Void had created the Twilight’s Hammer to bring about the End of all Things.
N’Zoth as he explained to Benedictus wants only his Black Empire restored but the Twilight’s Hammer will never allow that as they want only oblivion.
Furthermore N’Zoth was shown actively killing the World Soul in BfA(she only stopped dying when N’Zoth died) in order to deny the Jailer his prize instead of corrupting it like the Old Gods directly supervised by Dreadlords were doing.
Of course his Black Empire cannot tolerate Light(since Lothraxion is controlling it) and thus kills it’s followers and anyone else who defies him in his Horrific Visions.
N’Zoth is the kind of guy who is all “do not oppose me or you will die.”