The Forge of Souls is what is being used to extract Azerite from Azeroth (i.e.: it's siphoning Azeroth's blood en masse and channeling it into the Sepulcher). It was essentially draining her of life and leaving her vulnerable to Zovaal's attacks, and I think it's a fair assessment to say that if the Forge of Souls was not stopped, Azeroth's wound would hemorrhage until she died (as it would never heal and would drain her until nothing was left).
Regarding the Forge of Origination, I don't think the exact source of the power has ever been explicitly stated. So far as I'm aware, its purpose is to wipe life from the face of Azeroth, which the Keepers within regulated. However, the forge is also able to be reconfigured to affect specific places, such as what happened to Lei Shen and his armies. I think it would be reasonable to say that hijacking of the forge, in a way similar to what Deathwing had planned in Cataclysm, could kill Azeroth if the power was directed into the world instead of across the surface. Going back to its power source, it's possible that the source of power is Azeroth and this could be an instance similar to the ritual you noted in Chronicle (i.e.: the power of Azeroth being used against her).