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Cody Rhodes has primarily worked on SmackDown since winning the Undisputed WWE Championship at WrestleMania 38, as the Championship Has mostly remained on the blue brand of WWE. The promotion has introduced a separate World Championship for RAW in the form of the World Heavyweight Championship, which is also performing well.
Cody Rhodes defeated Roman Reigns at WrestleMania XL to win his first World Championship in WWE, and it was also his first world title from any major promotion. Since winning the World title, he has been projected as the face of WWE, and he is doing an excellent job as the prime champion of the promotion so far.

Bubba Ray Dudley praised Cody Rhodes' SmackDown run so far
We can expect him to continue his rivalry with Drew McIntyre on SmackDown right now, but eventually, he will get challenged by Roman Reigns at WrestleMania 42, as it stands. Professional wrestling Legend Bubba Ray Dudley recently talked about Cody's work so far in SmackDown and praised it. Speaking on "Busted Open Radio" Podcast, he explained the following;
Cody Rhodes is active on SmackDown after winning his first world title
"One of the things that allowed Cody to cut that great promo was the guy standing in front of him, Paul Heyman. Paul will bring out the best in just about anybody. You know you have to up your game on the mic when Paul is there and Cody did. Paul's not always going to be standing in front of [Cody], but this is the kind of Cody I need to hear. You use the word 'polished' earlier in the show.

He recently participated in the men's War Games match at Survivor Series
"I don't want polished, Cody. I want a little bit of an unkept, dirty, gritty, raw Cody, a passionate Cody, a birthright Cody. 'My dad invented this match. I have to win. I won't sleep at night if I don't win.' That's what I want to hear from Cody Rhodes. That's the intensity I want to hear from Cody Rhodes. The bass in his voice, a tiny bit forced, but I'll take it."
But one of the major complaints about Rhodes' Championship run so far has been the ultimate predictability. It is quite clear that he only drops his title in major events like WrestleMania and SummerSlam; apart from these stages, he will never drop the title. We seriously hope did scenario changes in the future.