Cook the Veggies: Heat the olive oil in a large Dutch oven or pot over medium heat. Add the onion, bell pepper, zucchini, and ½ teaspoon of the salt. Cook, stirring occasionally, until the veggies are softened and just starting to brown, about 5-7 minutes.
Add Remaining Ingredients: Add the cumin, garlic powder, and chili powder, stirring to coat the vegetables. Pour in the kidney beans, pinto beans, fire-roasted tomatoes, enchilada sauce, broth, and the remaining ½ teaspoon salt. Nestle the chicken into the mixture.
Simmer: Cover, bring to a rolling boil, then reduce to gentle simmer. Cook, covered, for 15-30 minutes, or until the chicken is cooked through and tender (timing will depend on the type of chicken and size of pieces used). Once cooked, remove the chicken to a cutting board and shred with two forks or dice into 1-inch chunks.
Partially Blend: Turn off the heat. Use an immersion blender to blend 1 to 2 cups of the soup directly in the pot. Alternatively, carefully transfer to a blender, blend on high, then return to the pot. This helps create a thicker, creamier base without added cream, while keeping plenty of texture.
Finish and Serve: Ladle one cup of the soup broth to a small bowl. Stir in the cream cheese and whisk until fully melted and smooth. Add the cream cheese mixture along with the cooked chicken back to the pot and stir to combine. Add the lime juice, stir, then taste and add more salt if needed. Ladle into bowls and top with whatever makes you happy!