Make the peanut-ginger sauce: combine peanut butter, 1/3 cup tamari or soy sauce, 1/4 cup toasted sesame oil, pickled ginger juice, gochujang, honey, 3 tablespoons lime juice, and the additional 1 tablespoon tamari or soy sauce in a blender or jar; blend or whisk until smooth, adding water a tablespoon at a time to reach desired pourable consistency.
Prepare the chicken: pat the sliced chicken dry and toss with 2 tablespoons toasted sesame oil, 1 tablespoon chopped fresh ginger, and the chopped scallions.
Cook the chicken: heat a large skillet over medium-high heat, add the chicken mixture and cook, stirring occasionally, until edges are browned and chicken is cooked through, about 5 minutes.
Add butter, the garlic, and 1 tablespoon tamari/soy sauce (if not already added with the sauce); cook for about 1 minute more until fragrant, then remove the chicken from the skillet and keep warm.
Make the mango-herb salsa: in a bowl, toss chopped mango, 1 tablespoon chopped pickled sushi ginger, lime zest and the 2 tablespoons lime juice, chopped cilantro, chopped basil, and a pinch of salt until evenly combined.
Assemble the bowls: divide cooked rice between bowls, top with the seared chicken, spoon over peanut-ginger sauce, add mango salsa and sliced avocado, and serve immediately with extra sauce as desired.