If you wander over to the Ao3 tags, the single biggest theme has to be the 'Ultimate Analyst uses his Ultimate Talent to analyze the Ultimate Hope.' Basically, it's a premise built around Izuru being this detached, hyper-observant force who studies Nagito's particular brand of obsessive madness like it's a fascinating puzzle. I've seen it play out in so many ways – maybe Izuru becomes fascinated by the sheer statistical improbability of Nagito's luck cycle, or he sees Nagito's obsession with hope as a complex psychological case study. The dynamic leans heavily into an intellectual power imbalance that's weirdly intimate because Izuru is seeing parts of Nagito even Nagito doesn't understand. Sometimes it bleeds into the trope where Nagito's bad luck creates a situation only Izuru can solve, forcing this reluctant, all-capable protector role. You'll find a lot of these stories framed as case files or detached observations slowly warming into something more human.
Another massive one is the post-canon fix-it, where they're the last two left on the ruined Jabberwock Island, forced into coexistence. It naturally pushes the 'domesticity amid desolation' angle, exploring how two extremely broken people might learn to function together when the whole world is gone. The themes here revolve heavily around healing, or the lack thereof, and finding a new purpose. Does Izuru, with all his talents, bother trying to 'fix' Nagito? Or does Nagito's hope obsession finally find a tangible target in Izuru himself? It can get pretty introspective and melancholy, but that's part of the appeal.
Finally, the 'mutual obsession' trope is huge, where it's less about romance and more about two distorted worldviews colliding and locking into place. Nagito sees Izuru as the ultimate embodiment of hope, and Izuru sees Nagito as the ultimate expression of chaotic, unpredictable humanity. It's a feedback loop that writers love to mine for intense, often unhealthy, psychological drama.