Pentecost & the Ascension
The reference to the Son of Man "sitting at the right hand of power" draws on the picture of the messiah's enthronement in Ps 110.1. The phrase "coming on the clouds of heaven" further explicates the exaltation and enthronement of the Son of Man, although the reference is often missed. Daniel records in Dn 7.13, "I kept looking in the night visions, and behold, with the clouds of heaven, one like a Son of Man was coming, and he came up to the Ancient of Days and was presented fore him."
The Son of Man's "coming on the clouds of heaven" is not a reference to Jesus coming back to earth on (or with or in) the clouds, but is a reference to the Son of Man coming to the heavenly throne room in heaven to be presented before God the father and given "dominion, glory, and a kingdom, that all peoples . . . might serve him" (Dn 7.13)
So both OT references in Mt 26.64 refer to Jesus' ascension and enthronement at God's right hand.
Jesus tells the high priest that he will see Jesus in this exalted position. The "seeing" here is not literally seeing Jesus at God's right hand (God the father doesn't have a physical right or left hand, after all), but instead will see evidence that Jesus has ascended and been enthroned.
Enter Pentecost. Peter expressly links the giving of the Spirit on Pentecost with Jesus' ascension: "Therefore having been exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, he has poured forth this which you both see and hear" (Acts 2.33).
Peter then quotes Ps 110.1 (vv. 34-35) and then concludes in v. 36: "Therefore let all the house of Israel know for certain that God has made him both Lord and messiah-- this Jesus whom you crucified."
Pentecost is evidence that Jesus has been exalted to God's right hand. From it, Israel is to "know for certain" that God has made Jesus both Lord and messiah.
The events of Pentecost vindicate Jesus' Mt 26.64 testimony before the high priest that he would see Jesus sitting at God's right hand, having come to God's throne on the clouds of heaven.
Pentecost isn't just the giving of the Spirit -- although it is that. It is the initial proof that Jesus now reigns over all in heaven, although he has disappeared from the earth. And it is, specifically, the evidence by which "all Israel" -- including the high priest with whom Jesus spoke in Mt 26.64 -- could see that Jesus was who he claimed to be.
More generally, and perhaps more speculatively, the evidence of Jesus' ascension is the giving of the Spirit and of spiritual gifts. I see no reason to limit the giving of spiritual gifts to the specific gift of foreign languages manifest in Acts 2 (1 Co 13.8). The gift of the Spirit to the Church produces a broad manifestation of that gift among God's people. But let's not forget the upshot of Pentecost: The Church's Spirit-filled service continues to provide evidence of Jesus' ascension (Eph 4.7-16, specifically v. 8).
That is, the evidence that Jesus reigns is the Church's service in and to this world. Jesus continues to reign and rule through the service of his body to the world. On the cross he served the world quite literally with his physical body. As enthroned, he continues to serve the world in and through the mystical body of his church. The church continues to redeem the truth of the testimony of Jesus to the high priest -- in Spirit-filled service to the world, the world sees Jesus sitting at the right hand of power, having come to his throne on the clouds of heaven.