Place the chicken breasts in the insert of the Instant Pot. Pour in the 1/4 cup of water and sprinkle with a pinch of salt.
Secure the lid and set the valve to sealing. Cook on high pressure for 15 minutes. Once the timer ends, carefully quick release the pressure.
Transfer the chicken to a large bowl. Use two forks to shred it into bite-sized pieces.
In a small bowl or measuring cup, whisk together the barbecue sauce, Italian dressing, and brown sugar substitute until smooth.
Return the shredded chicken to the Instant Pot. Pour the sauce mixture over the chicken and toss until evenly coated. For bolder flavor, set the Instant Pot to sauté and cook the chicken with the sauce for 3–5 minutes, stirring often, until heated through and slightly thickened.