Put chicken breast in the bottom of the Instant Pot liner. Pour the hot sauce and ranch of the chicken. Place the butter on top of the chicken.
Close the lid and set it to sealing. Pressure cook on HIGH for 10 minutes. It will take the Instant Pot about 10 minutes to come to pressure before the cooking time begins.
After cooking, allow for 5 minutes of natural release followed by a quick release. When all the pressure is released, open the lid. The chicken should reach a minimum internal temperature of 165°F. Remove the chicken, setting it aside in a medium-sized bowl.
With the Instant Pot set to Warm, place the softened cream cheese, shredded cheddar, and shredded mozzarella to the sauce in the pot, breaking up the cream cheese and whisking until the cheese mixture is smooth or mostly smooth.
Shred the chicken with two forks or a hand mixer and add it back to the pot, stirring it into the cheese mixture. Mix in Worcestershire sauce and onion powder.
Transfer to a serving dish such as a pie dish or a ceramic tart dish. Serve with a drizzle of ranch or hot sauce or top with blue cheese, green onions, or chives (optional).
Notes
To soften the cream cheese, leave it on the kitchen counter at room temperature for about an hour. Cutting the cream cheese into smaller chunks will help it soften faster.To soft the cream cheese quickly, you can microwave it by placing the unwrapped cream cheese on a microwave-safe plate and cooking it on high for about 15 seconds.