The War of the Ancients was the time when the Dragon Soul, and subsequently the Demon Soul, was forged by Neltharion (now Deathwing) and used as an ultimate weapon against the Burning Legion, the night elves, and the dragonflights all at once. The Dragon Soul held the power of the four flights and, potentially, the ability to hurt Deathwing himself. At the time of the War of the Ancients, Malygos, Ysera, and Nozdormu were all incredibly powerful aspects.
Three of the staff's stages mention two specific states -- the Arcane Orb and the Branch. Also, coincidentally, an item called the Timeless Eye has emerged from the datamined information. Each of these pieces relates in some way to Malygos, Ysera, and Nozdormu, respectively. The Arcane Orb is obviously tied to Malygos in some way (and, potentially, the new event at Coldarra featuring a new blue dragon), because he is the aspect of the arcane. The Branch, reminiscent of the world trees, could be linked to Ysera. The Timeless Eye is linked to Nozdormu, not only because of the time aspect, but his eyes are quite literally gemstones. In addition, the markings on the staff's base on the fabric are draconic runes, which could very easily be linked to the War of the Ancients and the greatest time of the dragons. These runes are also all over the Nexus.
All of these pieces lead to the potential conclusion that the new legendary staff is a combination of three of the four aspects' power that was also part of the Dragon/Demon Soul. Alexstrasza's influence could come from using the fire of the Red Dragonflight to forge the staff or potentially in some new piece that was stolen by Ragnaros or whatnot. Suffice to say, a lot of this speculation leads us to believe that War of the Ancients will be sooner than later, especially with this new information and speculation.
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