Peace Comes After the Storm
Simply put, Jesus did not experience fear and a lack of power and self-control; rather, as you pointed out, he experienced anguish (or stress, trouble, or agony). The infinite load of sin he was to bear in a few short hours was the reason for his anguish in the garden. Sin, as we know, is the very antithesis of peace. Peace, both peace with God and the peace of God, may seem absent during times of intense suffering, trials, and temptations, but it is there nevertheless--and perhaps most poignantly--after we endure whatever trial our loving Heavenly Father in His infinite wisdom places on us.
Jesus' poignant and loud cry from the cross (his fourth "word" from the cross) was
"Eloi, Eloi, lama sabachthani?" (Aramaic for "My God, My God, why have you forsaken me?")
Forsaken, But Not Abandoned
Was Jesus truly forsaken on the cross? Some Bible interpreters make the mistake (in my opinion) of insisting that Jesus, while on the cross, was literally forsaken by His Father for an unspecified amount of time. They call it "God turning His back on His one and only Son." I disagree. Jesus did, however, feel truly forsaken by His Father.
After all, Jesus was not only the divine Son of God, but he was also the Son of Man: fully divine and fully human . Where the one nature left off and the other began, we will likely never know. Scripture tells us, however, that he willingly subjected himself to his Father's will, whose will included not only the humiliation and self-emptying Paul addresses in Philippians chapter 2, but also his being tempted in all points as we Christians are, yet apart from sin (Hebrews 4:15).
I suggest the preternatural darkness which enveloped the land surrounding the cross for three hours starting at noon, bore silent but eloquent witness to the darkness which enveloped Jesus' spirit, soul, and body while he was bearing away the sin of the world (John 1:29 and 36).
Your question simply underscores one of many paradoxes in Scripture which are not easily--if ever--answered fully. The hypostatic union of divine and human is one of them. Another one is how the sinless, spotless Lamb of God could become sin for us; how the Just One could die for the unjust (1 Peter 3:18).
Moreover, the "power, love, and self-control" with which the Holy Spirit substitutes for our fear, were fully evidenced in Jesus,
while he was in the Garden of Gethsemane (and Gethsemane is poignantly apropos, since it means "olive press"),
while he was whipped mercilessly by Roman soldiers, and
while he was "lifted up" on a cruel cross so he could "draw all men to himself" (John 12:32).
Who but the Son of God in power could endure such intense suffering? Who but King Jesus could evidence such love (John 3:16)? Who but the Son of Man could exercise such self-control that he chose not to summon 12 legions of angels to rescue him from a painful death, but chose rather to earn his given name, Yeshua, meaning "God saves" or "God is salvation"? (Luke 1:31).
Jesus' Eyes Were on the Prize
In conclusion, Jesus' agony in the garden was not evidence of his being abandoned by the Holy Spirit; quite the opposite in fact. During the time that Jesus "was deeply grieved, to the point of death" (John 38), he was not only ministered to by an angel of God (Luke 22:43), but when he rose from his prostrate position, and with great resolve, he said to his dozing disciples,
"'Why are you sleeping? Get up and pray that you may not enter into temptation'" (Luke 22:46),
"'Get up, let us be going; behold, the one who betrays Me is at hand'" (Mark 14:42; Matthew 26:46).
Additionally, when Jesus finished his prayer in the garden with the words,
"'. . . yet not My will, but Yours be done'" (Luke 22:42; Mark 14:36; Matthew 26:39),
he was filled with peace, for as the writer to the Hebrews says in his description of Jesus' anguish,
". . . Jesus [is] the author and perfecter of faith, who for the joy set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God" (Hebrews 12:2).