Rinse rice thoroughly in cold water. Cook rice with water in a pot, cover, and simmer for 15 minutes. Let stand 10 minutes. Mix rice vinegar, sugar, and salt in a heatproof bowl; microwave for 30 seconds to dissolve sugar. Fold into hot rice to cool.
Preheat oven to 375°F (190°C). Toss tofu/tempeh cubes in cornstarch and tamari, then pan-fry in sesame oil until golden. Alternatively, bake for 20 minutes.
In a small bowl, whisk vegan mayonnaise, rice vinegar, tamari, and maple syrup for the sauce.
Assemble bowls: Layer seasoned rice, add cooked tofu/tempeh, and top with cabbage, cucumber, avocado, carrot, bell pepper, edamame, and panko breadcrumbs.
Garnish with scallions, sesame seeds, and drizzle with sauce before serving.