Heat butter in a large skillet over medium heat. Cook the chicken thighs for 5 to 7 minutes on each side until fully cooked and no longer pink. Once done, remove the chicken from the skillet and let it rest for about 5 minutes. Afterward, shred or chop the chicken into bite-sized pieces and set it aside for later.
Cook the bacon in a medium skillet over medium-high heat, turning occasionally, until crispy and browned, about 10 minutes. Once done, transfer the bacon to paper towels to drain, keeping 1 tablespoon of bacon grease in the skillet. Let the bacon cool for about 5 minutes, then crumble it into pieces and set aside.
Transfer the chicken drippings from the skillet into a stockpot or Dutch oven. Sauté the potatoes, carrots, celery, red onion, and garlic over medium heat until the onion becomes soft and translucent, about 5 minutes. Add the shredded chicken, bacon grease, broth, milk, mushroom soup, corn, paprika, salt, and pepper. Lower the heat and let the stew simmer for 20 minutes to allow the flavors to meld together.
Combine the baking mix and milk to create a sticky dough for the dumplings. Spoon the dough into the simmering stew. Let the dumplings cook uncovered for 10 minutes, then cover the pot and cook for another 10 minutes, or until the dumplings are fully set. Serve the stew topped with crumbled bacon for an extra burst of flavor.