Why did the Prophet, peace and blessings be upon him, pray Tarawih for only three days, while Umar ibn al-Khattab revived it for a full month?

The Prophet (peace be upon him) used to encourage people to perform Tarawih prayers and make them desirous of it, without obligating them. People would pray individually and in congregations in their homes and mosques. The Prophet (peace be upon him) led the people in congregational prayer for several nights, then he stopped going out to them, fearing that it might become obligatory upon them. The situation remained as such during the time of the Prophet (peace be upon him), the time of Abu Bakr, and the beginning of Umar's caliphate, until Umar gathered the people behind one Imam, Ubayy ibn Ka'b. The congregational Tarawih prayer has continued to this day. As for Qiyam al-Layl (night vigil) in general, it was obligatory at the beginning of Islam then abrogated, remaining a confirmed Sunnah, and it is more emphasized in Ramadan.