Sprinkle boneless skinless chicken breasts with salt. Add the chicken breasts to the Instant Pot. Add the remaining ingredients in order, through zucchini.
Secure the lid on the pot. Cook at high pressure for 18 minutes. Allow the pressure to naturally release for ten minutes, then use the manual release. Pull out the chicken breasts and add coconut milk. Switch Instant Pot to Sauté mode and stir to combine.
Dice or shred chicken, then return it to the soup. Serve hot, topped with garnishes of choice.
Slow Cooker Method: If you don't have an Instant Pot, you can make this Whole30 chicken tortilla-less soup in the slow cooker. Add all ingredients, except coconut milk, in order listed. Cook on low heat for 7 hours or on high heat for 4 hours. Remove chicken breasts and dice. Stir in coconut milk, then return chicken to slow cooker. Serve with garnishes.