Combine chicken breasts and broth in a multi-functional pressure cooker (such as Instant Pot(R)). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build. Release pressure using the natural-release method according to manufacturer's instructions for 10 minutes. Release remaining pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer chicken to a bowl and shred. Select Saute function. Add cream cheese, sriracha, ranch dressing, and chile-garlic sauce. Return shredded chicken to the pot. Slowly add Cheddar cheese, constantly stirring until melted and all ingredients are well combined. Select Keep Warm function until ready to serve. Garnish with green onions.