If Jesus needed to be saved from death himself then he cannot be a substitute for those who have also been condemned to die.
Common Christian thought on the matter is that, according to verses like 1 Peter 2:24, Jesus took the punishment for our sins that we deserve. However, I have seen very few people mention is that Jesus didn't go into eternal conscious torment in hell, which is another common Christian belief about what our punishment for sin is supposed to be. Therefore, either Jesus didn't take the punishment we deserve or the idea of what the punishment Jesus took on our behalf is not accurate. As a result, eternal conscious torment in hell is not accurate.
So what happened to Jesus? Hebrews 5:7 says, "During the days of Jesus’ earthly life, He offered up prayers and petitions with loud cries and tears to the One who could save Him from death, and He was heard because of His reverence."
However, Jesus was not saved from the physical death of the cross. No. God heard his prayer because Jesus reveres Him. God, in turn, saved Jesus from the death of his soul in the afterlife. Isaiah 53:9-12 says YHWH crushed Jesus and made his soul a sin offering. Jesus died, body, mind, and soul. But why would God allow this to happen?
This happened because only those who are guilty of sin deserve death according to Romans 6:23. Therefore, since Jesus never even sinned one time, yet death still received Jesus, death itself actually sinned. Now death can be destroyed. In the end, death itself will be cast into the lake of fire where it, too, will die as a result of its sin against God, according to Revelation 20:14. This legal loophole needed to be exploited to trick death into violating God's laws. Thus, it was impossible for death to hold Jesus in its clutches. Therefore, God resurrected Jesus.
So this idea about Jesus being the substitute is correct, not clearly explained very often.
What do we get out of it? In the age to come, those who are counted worthy, will be resurrected and receive the gift of eternal life, never to die again even if they wanted to, and will be children of God and a brother or sister to Jesus.
Luke 20
35But those who are considered worthy to share in the age to come and in the resurrection from the dead will neither marry nor be given in marriage.
36In fact, they can no longer die, because they are like the angels. And since they are sons of the resurrection, they are sons of God.
So yes, Jesus did indeed need to be saved from death because he isn't God. Who Jesus is is God's holy one, His Messiah, His Servant, and His Son.