Is “The novel fictionalizes that Zhang Yun was beheaded by Cao Cao due to Zhou Yu's counter-espionage scheme; in official history, he surrendered to Cao Cao with Liu Cong and was not killed.” true?

In official history, Zhang Yun and Cai Mao were both partisans of Liu Cong, the younger son of Liu Biao, and when Cao Cao marched south, they surrendered to Cao Cao with Liu Cong. 'When the太祖's army reached Xiangyang, Cong raised the province and surrendered' (Records of the Three Kingdoms, Book of Wei, Biographies of Dong, Er, Yuan, and Liu). Thereafter, official history has no record of Zhang Yun being executed by Cao Cao. However, in Chapter 45 of Romance of the Three Kingdoms, it is fictionalized that Zhou Yu used Jiang Gan's theft of a letter to implement a counter-espionage scheme, causing Cao Cao to mistakenly believe that Cai Mao and Zhang Yun were secretly communicating with Eastern Wu, and thus had Zhang Yun and Cai Mao beheaded together.