My theory is that the usual death entities like Bwonsamdi and others just collect souls into their own post-shadowlands realms to grow in power. They know they need life as a counter-force to keep balance (without life, there's no death). These entities usually despise undead because they break the cycle.
However, there's some unknown death entity that is either mad or too greedy and just wants to eradicate life or replace it with undead. It's either Helya or something above Helya (maybe the entity Odyn made a bargain with to learn Death's secrets). Either way, this entity seems have been weakened or dormant and Sylvanas is empowering it through genocide. Its ultimate goal may be indeed to kill the World Soul, which would ultimately foil the Old Gods' very purpose.
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During 7.3.5, there was a dialogue with Alleria in which she said she felt she died twice: once when they got lost in Draenor, and then when she consumed L'ura. She also says that she fears "death is the true legacy of the Windrunners".
So, the "three deaths" may not be literal dying. Her third "death" could be her being lost to the Void's influence.
Anyway, possible candidates for "her third death":
* Sylvanas: Died thrice already, but some people consider that her death by Arthas was actually her "birth" as the "Banshee Queen" and does not count.
* Alleria: "Died" twice metaphorically, as she herself acknowledges it. The "third death" may also be a metaphor.
* Azshara: Almost died in the Sundering, then on Nazjatar. Her true final demise may be the "Third Death".
* Helya: Died twice, once when Odyn turned her into a val'kyr, then when Odyn sent adventurers to kill her in Helheim. She's been growing in power in the background since, and may be the entity behind Sylvanas' actions.