Why the requirement for holidays in honor of God (Easter, Tabernacles, etc.) and detailed definitions of the celebration algorithm contained only in the Old Testament, but not in the New?
Old Testament requirements for such holidays were antitype of their fulfillment in the New Testament. Christ fulfilled all the requirements of the Law. He says, My Father works hitherto and I work. It behoves every New Testament believers to be actively involved in the services of the Lord ~ evangelism, teaching, counseling and caring for the hurt.
God is rich in all human beings and does not need anyone's services. We owe it to God worship and thanks for the blessings, and every person who does a good deed will benefit him before others.
I agree with Vincent's view. The coming of Christ has fulfilled the requirements of festivals of Old Testament. Christ is the reality of all sacrifices. In Apostle Paul's letters, he also emphasizes the abolitions of all festivals of Jews.
It is great when there is a celebration for Christmas and Easter, for example, in the Christian Church. It allows churches - and people in their own lives - to really proclaim the wonderous news that these festivals celebrate. Just image what it would be like if such commemorations did not happen in the same way because they were ordinary working days.
For a point of clarification: Easter is not a holiday that is commanded to be observed within the corpus of the New Testament. It became a holiday that was celebrated as the church began to create customs and liturgies to help teach the faith (socialization). As for the commanded observances of the Old Testament and their lack of presence in the New I would encourage you to examine the first half of the book of Romans and the book of Hebrews. But in short, like a military member graduates and leaves boot camp behind, the disciplines of the Old Testament served their purpose as the matter they pointed to was fulfilled: the arrival and work of the Messiah.