Place the chicken breasts in the Instant Pot in a single layer.
Sprinkle the garlic powder, onion powder, and paprika evenly over the chicken; season with kosher salt to taste.
Pour 1 cup chicken broth over the chicken, then add 2/3 cup of the BBQ sauce on top.
Secure the lid and set the valve to sealing. Select Manual/Pressure Cook on high and set the time for 15 minutes.
When cooking finishes, allow a natural pressure release for 10 minutes, then carefully quick-release any remaining pressure.
Check the chicken temperature with a meat thermometer; it should read at least 165°F. If needed, cook a few minutes longer.
Remove the chicken to a cutting board or bowl and shred with two forks.
Return the shredded chicken to the Instant Pot, add the remaining 2/3 cup BBQ sauce, and toss to coat; adjust salt to taste before serving.
