As soon as Therald was ousted from the battle, Edwin took a leap onto the beetle and ordered it to fly higher.
He decided to join the other two who were currently being overpowered by Leah and help them in defeating her.
He wasn't underestimating Azzy at all. It was just that he was at his wit's end and doesn't have the confidence to deal with Azzy and his platinum grade Arcana, all by himself.
Fortunately, he was even able to escape the fog and flew toward his allies. However, Azzy didn't chase him. He stayed inside the fog.
Azzy doesn't want to deal with Edwin directly, fearing that he might kill him due to his hatred for Edwin's father, the late king of Northern Qudour. It is also the reason why he went after the beast, instead of its owner.
He thought that Edwin would admit defeat once his soul beast and his partner would be out of the battle.