The Rose and William rumour was started by the odious Dan Wooten in February 2019 in the Sun showbiz/gossip section (he was never a royal reporter), as the alleged falling out of the "Turnip Toffs" over Catherine wanting Rose to be sidelined. This rumour was not repeated in any other British publication because no other paper could find any evidence to substantiate the rumour.
The rumour took flight online, fueled by Hadley Freeman asking on Twitter in March 2019 what she was missing/failing to understand. The equally odious Giles Coren gave his infamous reply about the affair rumours being true - which he has repeatedly, subsequently stated was him making up shit whilst drunk, and that he has no connections with that circle of people to know anything - but too late. Coren's twitter nonsense was picked up by a certain Sussex squaddie and writer of fan fiction about the Sussexes, who posited that dog bowl gate was about W&H fighting over the alleged affair. She too tried to walk this back, but again, too late, since that particular rumour also went viral. And it was picked up in US and European publications as having some factual truth about it, but never in British newspapers.
During the "Where's Kate?" nastiness of March 2024, UK papers were reporting on what US publications, commentators like Colbert and WME sheep were parroting based on internet rumours. They were not reporting that the rumours had any basis in fact, only that they were being discussed.
Interestingly, it is alleged that Coren spent time with the Sussexes and their usual crowd of pals (including a pregnant Meghan) at the opening of Soho House in Amsterdam shortly before his infamous post in 2019.