When did the dragon get this authority to be able to delegate authority?
Apparently, it was around the time of Jesus as declared by the devil in
"I will give You authority over all these kingdoms and all their glory," he said. "For it has been relinquished to me, and I can give it to anyone I wish.
Jesus didn't correct him. All authority came from God.
10So Pilate said to him [Jesus], “You will not speak to me? Do you not know that I have authority to release you and authority to crucify you?” 11Jesus answered him, “You would have no authority over me at all unless it had been given you from above. Therefore he who delivered me over to you has the greater sin.”
Ultimately, the dragon got his authority from God as well.
1 John 5:19
We know that we are children of God, and that the whole world is under the control of the evil one.
Does he have this control today?
I think so until the return of Christ. Meanwhile, we are comforted by the words of Jesus in John 16:
“I have told you these things, so that in me you may have peace. In this world you will have trouble. But take heart! I have overcome the world.”