Spoilers: Background from the game's writer interview, including the Forge of Souls. No campaign ending.

The Poxmakers in Total War
Ku'gath leads the Poxmakers of Nurgle in Immortal Empires and in The Realm of Chaos. Both campaigns come with Total War: Warhammer III. Tamurkhan’s Maggot Host and Epidemius’s Tallymen are later Nurgle campaigns. They share a race and a taste for disease. They do not share his way of brewing it.
In battle he is a bulky ranged monster who also casts Nurgle magic. When Thrones of Decay rebuilt plagues, Ku'gath was the lord who could keep many Blessed Symptoms active together. His diseases are combinations. A single borrowed symptom is the smaller version of what his faction is built to do.
The sandbox war a player fights with the Poxmakers is not the record of his failure at Zhufbar. That older account explains who he is. The campaign map decides what he does next.
A maker, not a courier
The game’s lead writer sets Ku'gath apart from other Great Unclean Ones. They spread gifts Nurgle has already made. Ku'gath tinkers, tweaks, and tries to invent. The personality is a craftsman’s gloom rather than a reveller’s cheer. The work is the point.
The same account follows a Nurgling avalanche that Grand Paraoxus survived. Paraoxus fled across the sea to Grand Cathay, and Ku'gath went after him. In the Celestial Dragon Empire the plague-father is known as Zin-Fa the Ever-Pustulent, a name that belongs to Cathay’s courts. It is not the name of an Immortal Empires province.
Zhufbar and the Forge of Souls
Ku'gath was tasked with the fall of Zhufbar. He did not break the hold. Three rival greater daemons succeeded at the tasks set for them. Nurgle lost a wager to the other gods, and lost standing in the Great Game because of that failure. Ku'gath was banished to the Forge of Souls.
The Forge is not Skarbrand’s exile. The account gives Ku'gath a few centuries inside it, then keeps him among Nurgle’s favoured servants for as long as he goes on making poxes and plagues. Favour and failure sit together. He can still fail to crack a dwarf hold and remain the plague-father.
Other hands on Nurgle’s work
Tamurkhan binds chieftains into a host and rides the Toad Dragon Bubebolos. Epidemius counts infections as they spread and studies how a body fails. Festus the Leechlord serves the same god through the Warriors of Chaos. None of them is a lieutenant of the Poxmakers. In Immortal Empires they are neighbouring campaigns. In the fiction they are different servants.
Update 9.0 lets Archaon subjugate Ku'gath after defeating him, and gives the Poxmakers’ regions to a new Nurgle vassal. That is a campaign rule for the Everchosen. It is not a pardon from the Forge of Souls, and it is not the end of a player’s story written back into the older account.
Ku'gath Plaguefather: gameplay and availability · More character stories
Sources
- Who is Ku'gath Plaguefather — Total War — totalwar.com
- Thrones of Decay: Introducing Tamurkhan — Creative Assembly — community.creative-assembly.com
- Immortal Empires DLC Ownership Guide — SEGA — support.sega.com
- Update 9.0 release notes — Total War — totalwar.com