Story

Second Eruption
The Core of Wind first formed when the Will of the Honkai gave it to Sirin during the Second Eruption, it was and dubbed the Gem of Desire. Through Sirin the Core's Soul was supressed and the Authority was utilised many times. After Sirin's death her corpse and the Cores held by it were later found in the ruins by Schicksal.
Schicksal Experiments
After Otto found out Kiana had compatibility with Core of Death he put a stop to the experiments with it but still wanted to create a Herrscher. As a result he took the next test subject Wendy who had shown a 23% compatibility with the Core of Death and put her through the experimentation process but with the Core of Wind. The Core of Wind was successfully accepted by Wendy but she showed no signs of the powers and lost the use of her legs so was sent back to New Zealand with the Core still implanted in her and was relieved from duty.
New Zealand
While in New Zealand Wendy would interact with the Soul of the Herrscher of Wind a bit but due to the suppression from Sirin the Soul was weak so they generally stayed separate with each imprinting on each other's Souls little amounts. When Kiana, Bronya, and Mei were tasked with collecting the Core of Wind from Wendy, once she found out the location of the Schicksal forces coming to collect her, the Herrscher of Wind took over Wendy's body and ran off to destroy them. Through talking with the Herrscher of Wind, Wendy was able to come through multiple times, in doing so showing she was still there. After a long fight Cocolia appeared and struck down them all before capturing Wendy and Mei through a mind controlled Bronya.
ME Corp
Cocolia took Wendy to ME Crop to be experimented on. After some experimentation and being able to give her final words, Wendy was killed by Cocolia and the Core of Wind was extracted. The Core of Wind was then used by Cocolia to power the Mech Wotan before being taken by her as she fled.
The Deep
Cocolia who was working with World Serpent lured the Hyperion crew to the Deep with the promise of preventing the Core of Wind from getting in the hands of Otto and Schicksal who were attacking. She used this opportunity to toss the Core of Wind into the Sea of Quanta under the guise of keeping it safe but in reality it was where it could be obtained by Kevin. In response Bronya jumped into the Sea of Quanta to retrieve the Core.
Sea of Quanta
Once it fell into the Sea of Quanta it was located by Kevin who was able to use the Honkai energy it held to replenish his strength. Once the new Herrscher of Reason Bronya arrived to obtain the Core, Kevin was able to easily overpower and exhaust her and almost took her Core if not for Welt Yang appearing and confronting Kevin. As a result Kevin still with the Core of Wind in hand fled through the path opened by Bronya and escaped the Sea of Quanta.
World Serpent
While the Core of Wind was in the possession of World Serpent it was put in a status to prevent a new Herrscher of Wind awakening. This is where and how it stayed for a long time.
Herrscher of Finality
Once Kiana made the choice to become an artificial Herrscher of Finality she drew the Authorities from all the Cores with help of the Herrscher of Origin, through this she was able to get close enough to the Herrscher of Finality that the Cocoon of Finality granted her access to the Authority of Finality. Due to being artificial Kiana continued to require use of all other Authorities to wield the Authority of Finality, so the Core of Wind was drawn to Kiana it would be used to keep the connection alive, in the process continuing to be supress the Soul within the Core.