贪得无厌 is more idiomatic (preferable in a more literary writing style). 永不满足 is more straight forward (preferable in a sci-fi story narrative)
Drifters of this world are the collectors of forgotten knowledge, lost technologies and broken histories. Our Drifter is haunted by an insatiable illness, traveling further into the lands of Buried Time, hoping to discover a way to quiet the vicious disease.
这个世界的流浪者寻找被遗忘的知能，丢失的科技，和破坏的历史。被贪得无厌的疾病困扰的流浪者不得不深入埋葬时间之地，但愿能从这个残忍的疾病找到平安。
Suggestions:
forgotten knowledge --> 遗忘了的知识
lost technologies --> 失落了的科技
broken histories --> 残破的历史
vicious disease --> 狠毒的疾病
被贪得无厌的疾病困扰 sounds like the illness are the greedy one that does the troubling. It should be 被贪得无厌这疾病困扰. (are troubled by the disease of insatiable greed)
从这个残忍的疾病找到平安 means 'to find peace from this cruel disease', 'to quiet the vicious disease' should be translated as 让那狠毒的疾病平静下来
My Translation:
这个世界的流浪者是遗忘了的知识，失落了的科技，和残破历史的收集者。
被贪得无厌这疾病困扰的流浪者不得不深入埋葬时间之地，希望能让这狠毒的疾病安静下来被永不满足这疾病困扰的流浪者不得不深入埋葬时间之地，希望能让这狠毒的疾病安静下来
Edit:
Illness here is a metaphor for 'bad habit' and 'insatiable' here doesn't imply 'greedy' but 'insatiable desire'. The desire of satisfying curiosity and the urge for adventure. I suggest 永不满足 over 贪得无厌