Rinse the jasmine rice until water runs clear. Combine rice and 1 1/2 cups water in a small saucepan, bring to a low boil, then reduce heat to low and simmer, covered, for 12–14 minutes until water is absorbed. Remove from heat, fluff with a fork, stir in 1 teaspoon toasted sesame oil and 1 tablespoon sliced scallions, then cover and keep warm.
Whisk together gochujang, soy sauce, honey, 1 tablespoon sesame oil, 1 tablespoon rice vinegar, grated ginger, minced garlic and lime zest in a bowl until smooth. Reserve 2 tablespoons of the glaze for serving and set aside.
Pat the salmon dry and place skin-side down on a plate. Spoon about half of the remaining glaze over the flesh side and let it sit at room temperature for 10–15 minutes to hydrate and lightly marinate.
While the salmon rests, make quick pickles: toss cucumber slices with rice vinegar, sugar and 1/4 teaspoon salt in a shallow bowl. Let sit at room temperature for at least 10 minutes, tossing once; chill briefly if you prefer them cold.
Preheat the air fryer to 400°F (200°C) for 3 minutes. Spray or brush the basket lightly with oil to prevent sticking. Place salmon fillets skin-side down in a single layer without crowding.
Air fry the salmon at 400°F for 8 minutes. After 8 minutes, quickly brush the tops with the remaining glaze, then continue to cook 2–3 minutes more until the salmon flakes easily with a fork and the glaze is tacky. Total cook time will be about 10–11 minutes depending on thickness.
Transfer salmon to a plate and let rest 3 minutes. While it rests, drain any excess liquid from the quick-pickled cucumbers and toss with a pinch of the remaining salt and the toasted sesame seeds.
Assemble bowls: divide the sesame rice among 4 bowls, top each with a salmon fillet (flaked if desired), a spoonful of pickled cucumbers, a drizzle of the reserved glaze, sliced scallions and extra sesame seeds. Serve with lime wedges on the side.