If we follow the pattern set forth in Scripture, we should pray to the Father, as Jesus taught us both in Matthew 6 and as He taught by example in His prayers. We also should pray in the name of the Son, as Jesus also taught in John 16:23-24. This was the pattern the Apostle Paul gives us in Ephesians 3:14-21. Ephesians 2:18 tells us that through Christ both Jews and Gentiles have access to the Father in the Spirit. So, my view is that the general pattern of prayer is to pray to the Father in the name of Jesus. In my prayers, I almost always spend some time thanking the Father for Christ, who is the greatest blessing given to us.
However, I do not think it is wrong if one prays directly to Christ Jesus or to the Holy Spirit. While I know of no examples in Scripture where prayer is directed to the Holy Spirit, I do not find the concept to be contrary to Scripture. I note that in Acts 7:59, when Stephen was dying, His prayer was directed to the Lord Jesus. And the Apostle John closes out the book of Revelation with a prayer to the Lord Jesus. So, there is certainly valid precedence for praying to Jesus. The Holy Spirit, being our comforter and friend, certainly is capable of having conversation with us as well.
Nevertheless, given the teaching of Christ, I believe that His pattern to us is to pray to our Father in heaven. And we should ask in the name of Jesus, a pattern that Jesus explains in John 16:26-27 as being based on the Father’s own love for us, which love is shared by the Son and the Spirit. As Hebrews 4:15-16 states, we have the privilege of coming boldly to the Father because of our great high priest, Jesus Christ.
I appreciate your observation on the “Christ focus” of Scripture. Both the Father and the Spirit point to the Son. He is everything to us, our wisdom, our righteousness, our sanctification, our redemption, our hope, our life, our shepherd, our brother, our friend, and our Lord and our God. Hebrews 12:2 tells us to look to Him as the author and perfecter of our faith.