According to Fightful Select, the producers for the latest edition of WWE SmackDown (3/3/2023) have been revealed:

Michael Hayes produced the segment featuring Cody Rhodes and Roman Reigns.
The match between Rhea Ripley and Liv Morgan was produced by Petey Williams.
Jason Jordan was the producer for the Dominik Mysterio vs. Santos Escobar match.
Adam Pearce produced the promo segment featuring Drew McIntyre, New Day, Karrion Kross, LA Knight, and Sheamus.
Kenn Doane, also known as Kenny Dykstra, produced the match between Tegan Nox and Shayna Baszler.
Michael Hayes also produced the match between Sami Zayn and Solo Sikoa.
Jason Jordan produced a dark match featuring Cody Rhodes vs. Finn Balor for the show.
Another dark match on the show, featuring Charlotte Flair vs. Sonya Deville, was produced by Petey Williams.
Lastly, a dark match between Hit Row and The Brawling Brutes before WWE SmackDown aired was produced by Kenny Dykstra.