Preheat oven to 400° Fahrenheit. Adjust oven racks as needed to fit sweet potatoes and chicken simultaneously.
Rinse 4 large sweet potatoes under running water. Use scrub brush to remove any surface dirt. Once potatoes are clean, pat potatoes dry with paper towels.
Pierce each potato on all sides with tines of fork, creating small vent holes all over surfaces of potatoes. Set potatoes aside.
Place 2 medium boneless, skinless chicken breasts on cutting board. Trim chicken as needed. If chicken breasts differ in size or thickness, pound chicken with meat pounder or rolling pin until evenly thick.
Season chicken breasts generously on both sides with plenty of salt, then place chicken in baking dish.
Transfer prepared sweet potatoes and chicken to preheated oven, placing sweet potatoes directly on oven rack. Bake potatoes and chicken 15 minutes.
After 15 minutes, check chicken by inserting internal meat thermometer into thickest spot of each chicken breast. Continue baking chicken as needed, checking temperature every 2 to 3 minutes, until chicken reaches internal temperature of 161° Fahrenheit.
Once chicken reaches target temperature, remove baking dish from oven. Set chicken aside to rest 5 minutes. Continue baking sweet potatoes until potatoes are soft, approximately 20 to 30 minutes. Note: very large potatoes may need up to 40 minutes. Check potatoes regularly to avoid over-baking.
While chicken rests and sweet potatoes bake, add 3 tablespoons mayonnaise, 9 tablespoons hot sauce, 1 tablespoon ranch dressing, ½ teaspoon garlic powder, and ½ teaspoon salt to medium mixing bowl. Mix ingredients together until fully combined into smooth mixture. Set sauce aside.
After chicken has rested, shred chicken into small pieces using method of choice (see Notes). Add shredded chicken to bowl of prepared buffalo sauce. Add thinly-sliced white parts and light greens parts from 2 green onions to bowl and stir until all ingredients are incorporated and chicken is coated in sauce. Set bowl aside.
When sweet potatoes are soft, carefully remove potatoes from oven. Set potatoes aside just until cool enough to handle, then carefully slice each potato open from one end to other end. Lightly press ends of sliced potato in toward center to open potato more.
Stuff each sweet potato with desired amount of buffalo chicken. Top chicken with additional ranch dressing, dark green parts of thinly sliced green onions, and blue cheese crumbles, and serve immediately with celery sticks if desired.