I honestly think Claudio's storyline in the Death Riders is potentially the most interesting, although it's been subtle. Or, there is no storyline, and I'm just projecting, of course.
But last year, there was a match - I feel like it was during the Owen Hart tournament, to see who got the next shot at the men's world title. Bryan I think had already won a match and advanced in the tournament, and he was on commentary for a match of Claudio's. But Claudio lost - and Bryan was shocked, and Claudio was obviously deeply disappointed, and he walked away without even really looking at Bryan, while Bryan was trying to yell at him that it was okay - these things happen, you win some you lose some.
And then Bryan did advance in the tournament, and talked about his intention to challenge for the world title again and hopefully get it - and you could see that Claudio wasn't happy about it, in the promos, and walked away from Bryan again. In backstage clips he claimed it was because of Bryan's health, and how he couldn't sit by and watch his friend put himself at such massive risk chasing more gold and pretend to be cheerleading that and okay with it - but combined with how he reacted when he lost in the tournament, it seemed like it was possible that wasn't the real reason, or not the only reason.
And then when the BCC turned on Bryan and became the Death Riders, Claudio did a few backstage promos talking about how great it was now, because he used to care and get frustrated when he lost and that he hadn't had any gold yet in AEW - but now he just felt nothing, win or lose, because he had a cause and a higher purpose to dedicate himself to. And that all sounded good and potentially noble, but also felt like maybe he was looking for a way to avoid feeling like a failure because he wasn't just running roughshod over everyone else, and getting titles. Because he hadn't had the success he wanted. And maybe he was looking for a way to convince himself, or at least everyone else, that it wasn't important, by trying to support Moxley and his 'cause' instead. But the fact he was still bringing up winning and losing suggested he did care about it.
Now the DR are in a position where Moxley's not the world champ, winning every match, anymore. Claudio, Yuta and Pac aren't the Trios Champs anymore. Most of the Death Riders are having some success but also taking some L's - except Claudio, who's been doing pretty well in his own matches lately. And supporting the rest of the DR to their wins a lot of the time. And maybe he did believe in Moxley's vision, but he doesn't anymore - or maybe he never truly believed it, and he feels like he can't ride the train of the Death Riders, avoiding blame for any of his individual losses because it's how the whole group does that matters, anymore. And he's doing well enough, on his own, to want to step out and just look out for his own performance again.
It's also true that Wheeler Yuta wavered on joining the DR, when it was just about Moxley and his cause, and seemingly only did in the end because Claudio said "you should trust me - have I ever steered you wrong?" Now he seems to be looking to Claudio for decisions more than Mox. I feel like whatever direction Claudio goes in, Yuta and probably at least some of the others will follow.
But I also think still waters may run deep in his case. Who knows what's going on in his head?