It seems to me that Jesus gave up his divinity when He became a man. He was still God and man but in order to pay the price to redeem us he had to do it as a sinless man. I don’t believe he ever used His divine power to do any of the works that He had done, but that He operated only in faith. Otherwise Satan could have said he (God) was operating illegally in the Earth.
That’s correct. In order to redeem mankind, He could only work in the manner of a man, becoming in effect Adam’s next of kin, his Kinsman Redeemer. So He set aside His divinity while on Earth, doing His miraculous work through the power of Holy Spirit.
This is the point of the wilderness temptation. Satan was tempting Him to use His divine powers, thereby violating the provisions of His mission (Matt. 4:1-11). It’s also why He accused the pharisees of blaspheming the Holy Spirit when they attributed His miracles to Beelzebub (Matt. 12:22-32). And finally it’s why He could tell his disciples that they would do even greater things than He had (John 14:12). He was sending the Holy Spirit to them.