Slice the onion into thin half-moons and the bell peppers into strips of the same thickness, then mince the garlic. Rinse and drain the black beans, squeeze the lime, chop the cilantro, and whisk together all the fajita seasoning ingredients in a small bowl.
Pat the chicken breasts completely dry with paper towels and slice any thick breasts in half horizontally. Sprinkle half of the fajita seasoning evenly over both sides and press it in with your fingers.
Heat 1 tablespoon of olive oil in a Dutch oven over medium-high heat and sear the chicken for 2 to 3 minutes per side until golden brown. Transfer the chicken to a plate and leave the browned bits in the pot.
Reduce the heat to medium, add the remaining olive oil, and cook the onion and bell peppers for 5 to 6 minutes until softened but still bright. Stir in the garlic for 30 seconds, then add the remaining fajita seasoning and stir for 30 seconds to bloom the spices.
Pour in the fire-roasted diced tomatoes with their juices, the diced green chiles, and the chicken broth, scraping up the browned bits with a wooden spoon. Nestle the seared chicken back into the pot and bring to a full boil over high heat.
Reduce the heat to medium-low, partially cover the pot, and simmer gently for 15 to 20 minutes until the thickest part of the largest chicken breast reaches 165°F on an instant-read thermometer.
Move the chicken to a cutting board and shred it into bite-size pieces. Stir the drained black beans and frozen corn into the pot and simmer uncovered for 5 to 7 minutes, then return the shredded chicken and any juices to the pot.
Turn off the heat and stir in the fresh lime juice and chopped cilantro. Taste and add a pinch more kosher salt or cayenne if needed, then let the soup rest for 5 minutes before serving.
Ladle the hot soup into bowls and top with sliced avocado, shredded cheese, sour cream, extra cilantro, and crunchy tortilla strips. Serve with a lime wedge on the side.