Preheat the oven to 400°F (200°C).
Add the rice to a parchment-lined baking sheet. Drizzle with the soy sauce, sesame oil, and chili paste. Toss until evenly coated, then spread into a thin layer.
Pat the tofu dry and grate or crumble it onto a second baking sheet. Drizzle with the soy sauce and oil, then sprinkle with the cornstarch (if using), garlic powder, onion powder, smoked paprika, salt, and pepper. Toss to coat and spread into an even layer.
Bake both trays, tossing halfway through, until golden and crispy. Use separate trays to avoid overcrowding and help everything crisp evenly.
Meanwhile, whisk together the soy yogurt, mayonnaise, sweet chili sauce, lime juice, smoked paprika, and sriracha (if using). Add a splash of water until the dressing reaches a pourable consistency.
Add the cucumber, edamame, green onions, and avocado to a large bowl.
Add the crispy rice and crispy tofu. Pour over the dressing and toss gently to combine.
Top with sesame seeds, chopped peanuts, and extra sriracha if desired. Serve immediately.