You are correct in linking Peter's description of Jesus's anointing "with the Holy
Spirit and with power" to Jesus's baptism by John the baptizer.
Reasoning logically we can safely assume that if kings and priests (both then and now) experienced a ceremonial investiture, which is defined as a "formal ceremony of conferring the authority and symbols of a high office," how much more would the King of kings, Lord of lords, and "priest of the Most High God" be entitled to, and worthy of, an investiture (see 1 Timothy 6:15; Revelation 17:14; 19:16; Hebrews 7:1 ff.).
That investiture was enacted in three installments and will yet be enacted in a fourth installment:
In Eternity Past
I will declare the decree: the Lord hath said unto me, "Thou art my Son; this day have I begotten thee" (Psalm 2:7 KJV; cf. Acts 13:33; Hebrews 1:5; 5:5).
The writer to the Hebrews, in keeping with his theme of the superiority of Christ to the Old Covenant, paints a word picture of what transpired in eternity past, when the eternal Father turned, as it were, to the eternal Son and said,
Son, today is the day I present you to the angelic hosts, whom we have created. They will worship you for reasons they do not quite understand yet, and they will minister to you as they minister to me.
One day, however, I will create image bearers who, unlike the angels, will worship you and me for saving them from themselves, since they will--as Satan and his legions did--rebel against me.
Then, in the fullness of time, I will honor your request for me to send you to earth to make right the wrong which Lucifer committed and which my human image bearers will perpetuate. You will empty yourself of many of your divine prerogatives by becoming fully human, because only as a flesh-and-blood human being will you be able to atone for the sins of my image bearers and make reconciliation between them and me possible.
Granted, I have used my sanctified imagination in describing something which is likely indescribable. Yet the investiture of the Son as Prophet, Priest, and King occurred in the eternal counsels of God, before the foundations of the earth were laid and before sentient creatures were created, celestial creatures first, and terrestrial creatures second.
In Space and Time, ca. September, 25 AD
And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased (Matthew 3:16-17).
When Jesus insisted John baptize him, Jesus did not do so as an act of repentance, for he had nothing of which to repent. He did so as a way to indicate to John, to assorted witnesses, and to his Father that in three short years, he would be baptized into a very real death in keeping with his primary purpose of coming to earth: To seek and to save and redeem lost sinners by dying in their place (see Matthew 20:22-23).
As in eternity past, when the Father presented his Son to the angelic hosts (Jesus's “coming out,” as it were), the Father was also present at his Son's baptism, giving Jesus his imprimatur to all Jesus would say and do during his three years of public ministry, a ministry that would culminate in his death, burial, resurrection, and ascension.
While God's words to the Son in Psalm address him simply as “Son,” at Jesus's baptism the voice from heaven adds the words “This is my Son” the words whom I love and with him I am well pleased (in all three Synoptics; Matthew 3, Mark 1, and Luke 3).
Notice the prominence of the presence of the Holy Spirit at Jesus's baptism. The Gospels tell us that the Holy Spirit of God descended from heaven and alighted on Jesus in the form of a dove. They tell us Jesus was not only led of the Holy Spirit into the wilderness (or desert), but Mark tells us that the Spirit sent (or as the NET Bible puts it, drove) Jesus out into the desert, and Luke tells us that after Jesus's baptism Jesus was “full of the Holy Spirit.”
For the next three years, Jesus's ministry to the world would be primarily as a prophet, and as such his followers described him as “a prophet mighty in deed and word in the sight of God and all the people” (see Luke 24:19 NASB). His mighty words and deeds were no doubt made possible by his utter dependence on his Father and on the anointing and induement of the Holy Spirit of God.
In Space and Time, ca. April, 27 AD
After six days Jesus took with him Peter, James and John the brother of James, and led them up a high mountain by themselves. There he was transfigured before them. His face shone like the sun, and his clothese became as white as the light. . . . While he was still speaking, a bright cloud enveloped them, and a voice from the cloud said, “This is my Son, whom I love; with him I am well pleased. Listen to him” (Matthew 17:1, 2, and 5 NIV; cf. Mark 9:2-8 and Luke 9:28-36a).
Notice that this investiture involved Jesus's clothing (vestments!?) which the Synoptics record “shone like the sun,” “became white as the light,” “became dazzling white,” and became “as bright as a flash of lightning.” Again, the Father re-confirms his pleasure in and his love for the Son, but he adds the words, directed to the inner circle of Peter, James, and John, “Listen to him” (i.e., Jesus).
Leading up to Calvary, Jesus's words would become increasingly important and significant, since his time on earth was quickly coming to an end, yet his disciples failed to listen, really listen.
Several times Jesus predicted his death at the hands of the elders, chief priests, and scribes (Mark 8:31; 10:33; Luke 9:22), but not until after his resurrection were the disciples able to understand the import of what Jesus had predicted (see Luke 24:44-49 in particular).
In space and time, date as yet unknown
And I saw heaven opened, and behold a white horse; and he that sat upon him was called Faithful and True, and in righteousness he doth judge and make war.
His eyes were as a flame of fire, and on his head were many crowns; and he had a name written, that no man knew, but he himself. And he was clothed with a vesture dipped in blood: and his name is called The Word of God. And the armies which were in heaven followed him upon white horses, clothed in fine linen, white and clean. And out of his mouth goeth a sharp sword, that with it he should smite the nations: and he shall rule them with a rod of iron: and he treadeth the winepress of the fierceness and wrath of Almighty God. And he hath on his vesture and on his thigh a name written, King Of Kings, And Lord Of Lords (Revelation 19:12-16, my bolding).
In keeping with the theme of investiture, I draw attention to the role vesture played in Jesus's appearance, as the apostle John described him, as one whose “eyes were as a flame of fire”; whose head was crowned with “many crowns” (mere earthly potentates require but one crown!); whose vesture was dipped in blood; whose name was “The Word of God”; and in whose train were the armies of heaven seated upon “white horses.”
I also draw attention to the name which appeared on both his vesture and his thigh, and that name was “King of Kings” and “Lord of Lords.”
Quite obviously, Jesus's role in the fearsome Day of the Lord is that of a conquering warrior-king whose task is to “smite the nations” and “rule them with a rod of iron.” Once that task is completed, “the kingdom (or kingdoms) of this world will have become the kingdom of our Lord, and of his Christ; and he shall reign for ever and ever” (Revelation 11:15 NASB).
In conclusion, one might be tempted to say that Jesus's first anointing (or investiture) in heaven was a precursor to all three of Jesus's roles as prophet, priest, and king. As for the anointing at his baptism, we could say it constituted his anointing as a prophet. As for his anointing as priest, we could say that that occurred on the Mount of Transfiguration, where again the voice of God announced his love for, and his pleasure in, his Son, and then told Jesus's inner circle to “Listen to him” (Matthew 17:5).
The investiture of Jesus as a conquering warrior-king will occur one day yet future, after which Jesus will defeat his enemies, making them a footstool for his feet (Psalm 110:1; Luke 20:43; Acts 2:35; Hebrews 1:13 and 10:13).