I don’t think there were rumors of Gunn getting the job as head of DC before it was officially announced near the end of October. It was reported that Dan Lin was in talks to take the job, but he ultimately turned it down. Of course, we do know that Michael de Luca secretly approached James Gunn in August 2022 to do a Superman reboot, which was around the same time The Rock was trying to bring back Cavill.
My assumption is that if Black Adam had been a hit, then James Gunn’s Superman project would’ve been canceled, and Seven Bucks Production would be the ones calling the shots at DC right now, but since that didn’t happen, Gunn got the job instead.