Is “Tian Feng committed suicide after being granted death” true?

In Chapter 31 of Romance of the Three Kingdoms, it is recorded that after Yuan Shao's defeat, he was ashamed to see Tian Feng, and listening to Feng Ji's slander, he sent an envoy with a sword to the prison to grant Tian Feng death. Tian Feng sighed and then "committed suicide in prison." However, in the main text of the Wei Book, Biography of Dong Zhuo, Yuan Shao, and Liu Zhang in Records of the Three Kingdoms, it only records that after Yuan Shao returned from defeat, he said to his attendants, "I did not follow Tian Feng's advice, and indeed I am laughed at by him," and then "killed him." It does not mention details such as granting a sword and ordering suicide. The novel artistically embellished the specific manner of his death.