I've seen a few different approaches to this, and they all hinge on how you interpret the concept. Some writers lean into the multiverse angle, with different Midoriyas from divergent timelines meeting. That can get pretty philosophical, fast—what does it mean to meet yourself? Are you jealous of the version that got a quirk earlier, or pity the one who suffered more? The conflict is all internal, which is tough to write well.
Another take is the clone or duplicate scenario, often from a villain attack or support item malfunction. That one's usually more about practical problems and emotional doubling. Does he feel twice the guilt, twice the responsibility? I read one where the two Dekus had to decide which one got to keep the 'real' life, and it was heartbreaking because they both wanted the other to have it. The self-sacrifice instinct turned inward.
Then there's the metaphorical or psychological version, where it's less literal and more about Izuku confronting his own self-image, his shadow self, or his past/future self through visions or mental landscapes. Those can be super introspective and quiet, almost like a character study dressed up as a supernatural encounter. The relationship isn't romantic in a traditional sense, but it's deeply intimate because it's literally with himself.
Honestly, I'm less convinced by the straight-up romantic pairings of two identical Dekus—it feels like it misses the point. The interest for me is in the duality and the internal dialogue, not just creating a mirror for shipping purposes. The best fics use the setup to explore his character fractures.