Before starting, set cream cheese and ranch dressing on the counter to reach room temperature (about 30 minutes). Chop celery and bell peppers into bite-sized pieces. Trim any fat from chicken breasts.
Press the sauté button on your Instant Pot. Add butter and let it melt until gently bubbling (not browning).
Add celery, bell peppers, and minced garlic to the pot. Sauté for 3-4 minutes until softened but still slightly crisp. The garlic should be fragrant but not burnt.
Add chicken breasts directly to the pot. Sprinkle paprika, garlic powder, and onion powder over everything. Pour in all 32 ounces of chicken broth. Give it a quick stir to distribute spices.
Lock the lid and ensure the pressure valve is sealed. Set to manual high pressure for 20 minutes. The pot will take about 10 minutes to build pressure before the timer starts.
When the timer beeps, allow natural pressure release for 5-10 minutes. Then carefully flip the valve to manually release remaining pressure. Be cautious of hot steam.
Remove chicken breasts with tongs and place on a cutting board. Use two forks to shred into bite-sized pieces. Set aside.
Add room-temperature cream cheese, buffalo sauce, ranch dressing, and shredded cheddar to the hot broth. Whisk vigorously for 1-2 minutes until completely smooth with no lumps. The soup will turn a gorgeous orange color.
Return shredded chicken to the pot and stir until mixed through. Taste and adjust seasoning with additional salt or buffalo sauce if needed.
Ladle into bowls and top with desired toppings: extra cheddar, green onions, buffalo sauce drizzle, sour cream, or ranch dressing.