How real is the tragic love story of Yu Ji committing suicide?

According to "Historical Records" and "Zizhi Tongjian", Xiang Liang killed people to avoid disaster and took Xiang Yu from the bottom to Wuzhong, which is today's Suzhou. The Yu family was named Kuaiji County. {At the end of the Qin Dynasty, the Wu and Yue areas in the Spring and Autumn Period were designated as Kuaiji County, and Wu (now Suzhou) was used as the county to govern the prominent families in Wuzhong. Xiang Liang's uncle and nephew made friends with the children of Jiangdong here. Yu Ji, a beautiful woman from the Yu family in Wuzhong, admired Xiang Yu's fame, married Xiang Yu, and stayed with him. Or it can be said that Xiang Yu was lucky enough to know Yu Ji and get this beauty. In October 202 BC, Xiang Yu led his army to retreat eastward, and Liu Bang led his army in hot pursuit. In December, the Chu army was surrounded by Gaixia (southeast of today's Lingbi County, Anhui) and was in a helpless situation. In order to further shake and break the will of the Chu army, Han Xin asked the Han army to sing Chu songs in the night. The Chu army all shed tears after hearing this, and Xiang Yu was also shocked, thinking that the Han army had occupied Chu territory. While he was drinking, he sang a song passionately and impassionedly. The song said: "Strength can lift the mountain and the world is overwhelming, but the times are not good and the glory will not fade away!" What can be done if the virtue is not gone? Yuxi, Yuxi, what can I do! Yu Ji also stood up and sang in harmony. The song said: The Han soldiers have captured the territory, and the songs of Chu are heard from all directions. The king is exhausted, how can I survive as a lowly concubine? After singing, he drew his sword and killed himself. Today, there is Yu Ji's tomb 15 miles east of Lingbi County, Anhui Province and on the south side of Provincial Road 303. If there was no such person, who would be sleeping in Yu Ji’s grave today? Didn’t the ancients have to make up stories to deceive us children?