Fit Instant Pot with trivet insert, then pour ½ cup water in bottom of Instant Pot. Place uncooked chicken breasts on trivet (okay to stack if needed), then cover chicken with ½ cup hot sauce.
Secure lid on Instant Pot with valve in Sealing position. Set Instant Pot to Manual High Pressure for 10 minutes. Instant Pot will pressurize and then cook time will begin.
After 10-minute cook time is up, Natural Release pressure for 5 minutes, then carefully Quick Release any remaining pressure. Carefully remove lid and transfer chicken to large bowl or cutting board. Shred chicken as desired (see Notes).
Empty any remaining hot sauce and water from Instant Pot, rinsing pot if needed before returning to Instant Pot. Set to Sauté mode and allow pot to heat up.
When Instant Pot is warm, add ranch dressing, softened cream cheese, remaining ½ cup hot sauce, and garlic sauce to pot. Stir until mixture is completely smooth.
Add shredded cheese to Instant Pot. Continue stirring until shredded cheese is completely melted.
Once cheese has melted and combined with other ingredients, return shredded chicken to Instant Pot. Stir until all ingredients are fully incorporated, then transfer buffalo chicken mixture to serving bowl or cast-iron skillet.
Garnish buffalo chicken dip with blue cheese crumbles and chopped green onions if desired. Serve warm with tortilla chips, crackers, and/or veggie sticks.