Care to elaborate? I've done the machine gun quest that introduces you to the forges as such, however no other forge quests are available. I have the first 3 keys inserted into the box after gaining maximum temper, however as the forges are now on a daily rotation there aren't quests to unlock each one anymore.
Oh then idk, I stopped playing when izanami forge came out and once I completed the quest for it I got the key mold. Maybe it is bugged if those quests are unavailable