Mix the sliced red onion with the lime juice and 1/4 teaspoon salt in a bowl; set aside. Pat the shrimp dry and season with salt and 1/2 teaspoon chili powder. Heat 2 tablespoons olive oil in a large pot over medium-high heat. Add half the shrimp and cook, until opaque, about 1 minute per side. Remove with a slotted spoon and transfer to a plate. Repeat with the remaining shrimp. Tent with foil to keep warm.
Add the remaining 1 tablespoon olive oil to the pot. Add the chopped red onion and cilantro stems and cook, stirring, until softened, about 3 minutes. Stir in the remaining 1 1/2 teaspoons chili powder. Add the tomatoes and cook until starting to soften, 2 to 3 minutes. Add 1 cup water, the chicken broth, potatoes and a big pinch of salt. Cover and bring to a boil. Uncover and reduce the heat to a simmer; cook until the potatoes are tender, 8 to 10 minutes. Smash about half the potatoes with a potato masher. Simmer until thickened, 2 to 3 minutes; season with salt.
Stir the cilantro leaves into the red onion mixture. Divide the shrimp and soup among bowls. Top with the pickled onion, avocado and corn nuts; serve with lime wedges.