Why would Jesus need to be saved from spiritual death? He was facing the death of the cross. (Philippians 2:8)
Why would Jesus need to be saved physically when He knew He was the sacrificial lamb who came to die and redeem His people?
The answer to you question is in Hebrews. This below is a good start.
Heb 2:
5For it is not to angels that He has subjected the world to come, about which we are speaking.
6But somewhere it is testified in these words:
“What is man that You are mindful of him,
or the son of man that You care for him?
7You made him a little lower
a than the angels;
You crowned him with glory and honor
b
8and placed everything under his feet.”
c
When God subjected all things to him, He left nothing outside of his control. Yet at present we do not see everything subject to him.
9But we see Jesus, who was made a little lower than the angels, now crowned with glory and honor because He suffered death, so that by the grace of God He might taste death for everyone.
10In bringing many sons to glory, it was fitting for God, for whom and through whom all things exist, to make the author of their salvation perfect through suffering.
11For both the One who sanctifies and those who are sanctified are of the same family. So Jesus is not ashamed to call them brothers.
12He says:
“I will proclaim Your name to My brothers;
I will sing Your praises in the assembly.”
d
13And again:
“I will put My trust in Him.”
e
And once again:
“Here am I, and the children God has given Me.”
f
14Now since the children have flesh and blood, He too shared in their humanity, so that by His death He might destroy him who holds the power of death, that is, the devil,
15and free those who all their lives were held in slavery by their fear of death.
16For surely it is not the angels He helps, but the descendants of Abraham.
17For this reason He had to be made like His brothers in every way, so that He might become a merciful and faithful high priest in service to God, in order to make atonement
g for the sins of the people.
18Because He Himself suffered when He was tempted, He is able to help those who are being tempted.