Is “Did King Wen of Chu once cut open the stone to obtain the Heshi Bi, and after being defeated by Ba and attacking Huang, die from the bursting of an arrow wound?” true?

The Records of the Grand Historian, in the Hereditary House of Chu, records King Wen of Chu's military activities such as 'attacking Cai, capturing Marquis Ai of Cai and returning' and the historical fact of 'first establishing the capital at Ying', but does not record the specific process of his obtaining the Heshi Bi and dying from an arrow wound. In the Chronicles of the Eastern Zhou Kingdoms, in chapters such as the seventeenth and nineteenth, his life events are linked together and novelized, fabricating or dramatizing his cutting open the stone to obtain the 'Heshi Bi' (see the recollection in chapter ninety: 'King Wen of Chu heard Bian He's weeping, then took his stone, had the jade worker cut it open, and indeed obtained a flawless beautiful jade, which was made into a bi and named: "Heshi Bi"'), as well as the bizarre ending in his later years: 'The Ba troops took advantage and greatly defeated Chu. The King of Chu was shot in the cheek and fled... Then he moved his troops to attack Huang. The king personally beat the drum, the soldiers fought to the death, and defeated the Huang army at Jiling. That night, staying in the camp, he dreamed of the Marquis of Xi advancing with angry vigor... When he woke up, the arrow wound burst open, and blood flowed without stopping. He urgently ordered the troops to return, and reaching Qiu, he died at midnight.'