Saints hire Brendan Nugent as O-Line coach; WR coach Keith Williams will return

Yep. And Venturi actually remained in New Orleans through two head coaching changes, and was a part of the coaching staff when the Saints won their first playoff game. Unusual, certainly, but wouldn’t be unprecedented if Rizzi ended up staying. (I still expect he’ll end up in Denver, but it would be great to have him back if all sides think that can work.).
If it were my choice, I'd talk to Moore about promoting Rizzi to a position of being exclusively an Asst Head Coach. He would be Moore's number one helping to coordinate offense, defense and special teams with an emphasis on preparing to be a head coach. I think that could be beneficial to both Moore and Rizzi.