Is it allowed if the Imam shortens the Taraweeh prayer?

Shortening the prayer in a manner that violates it is impermissible . As for shortening the prayer in a manner that doesn’t violate the prayer's rules, then there is no harm in this. The Sahabah lightened the Taraweeh prayer and prayed twenty-three Rak'at; This is because they lightened the way the prayer is prayed, but increased the number (of Rak’at). So there is no harm in shortening the prayer in a manner that doesn’t violate the prayer's rules. Rather, it is required because of the Prophet’s ﷺ saying: "Whoever leads the people in prayer, let him shorten it." However, shortening the prayer in a manner that invalidates the prayer is impermissible. And this nullifies the prayer, because he is not being at ease in prayer. The Prophet ﷺ saw a man praying who then came and greeted him; the Prophet ﷺ told him: "Go back and pray, for you have not prayed", until he did so three times. The man then said: "By Him who has sent you as a Prophet with the truth, I cannot do better than this, so teach me." So the Prophet ﷺ said: "When you get up to pray, say 'Allahu Akbar', then recite what is easy the Qur'an, then bow with calmness until you feel at ease, then rise (from bowing) and stand straight, then prostrate calmly (and remain in prostration) until you feel at ease." So this indicates that being in a state of ease is a pillar from the pillars of the prayer; it is not correct without it.