Why did Abu Bakr not gather the people for Tarawih prayer, while Umar did?

Tarawih prayer is a Sunnah (definition) by the consensus of scholars, and it is what is meant by the Prophet's saying (peace be upon him): "Whoever establishes prayers during Ramadan (definition) with faith and expecting Allah’s reward, all his past sins will be forgiven and all his future sins."

Abu Bakr did not gather people for it due to his preoccupation with fighting the apostates, or because he believed that it was better for people to pray in the last part of the night. As for Umar, he gathered people for it when Islam became well-established during his era, and the Salaf agreed upon the validity and affirmation of that.