The key is conveniently located nearby.From the locked storeroom door, turn around. You should see a pathleading over a stall and through an archway towards a tower adorned with Adyran flags. Climb up this tower. Hop along the platforms on the farside of the tower until you reach an open window. Climb inside.
Inside the room, you'll find the Storeroom Key, along with some food and a letter explaining who took it.
Return to the storeroom door and use the key to unlock it. Inside, you'll find a chest containing rewards to aid you in your Avowed journey.