Combine the soy sauce and fish sauce in a large bowl. Toss the tofu cubes in the mixture and let them marinate for 5 minutes.
Heat a large skillet or wok over high heat until it becomes very hot. Add the oil and swirl it around to coat the pan evenly.
Use a slotted spoon to transfer the tofu to the hot skillet, keeping the marinade aside. Cook the tofu without stirring until one side is golden brown, then stir-fry to brown the other sides evenly. This should take about 10 minutes. Once done, transfer the tofu to a bowl.
If the skillet looks dry, add a bit more oil. Add the diced onion, minced garlic, ginger, and chilies. Cook while stirring frequently until they become aromatic and begin to brown slightly, about 2 minutes. Next, add the napa cabbage and sugar snap peas, cooking them until softened, about 2 to 4 minutes. Stir in the cooked rice and press it down lightly with a spatula. Allow the rice to cook undisturbed for 1 to 3 minutes, so it develops a slight crust. Stir in the reserved marinade and cook for another 1 to 2 minutes to fully incorporate the flavors.
Create a well in the middle of the rice mixture and pour in the beaten eggs. Let the eggs cook, stirring gently, until they become slightly set, about 1 to 2 minutes. Carefully fold the cooked tofu back into the rice mixture and stir until evenly combined. Drizzle with lime juice, garnish with fresh cilantro or basil, and serve with lime wedges on the side.