Melt butter in a large skillet over medium heat. Cook chicken thighs in the hot butter until no longer pink in the centers, 5 to 7 minutes per side. Remove chicken and let cool, about 5 minutes. Shred or cut into small pieces and set aside.

Place bacon in a medium skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels, reserving 1 tablespoon bacon grease in the skillet. Let bacon cool slightly, about 5 minutes; crumble and set aside.

Scrape chicken drippings from the skillet into a stockpot or Dutch oven. Cook potatoes, carrots, celery, red onion, and garlic in the pot over medium heat until onion is soft and transparent, about 5 minutes. Stir in chicken, reserved bacon grease, broth, milk, mushroom soup, corn, paprika, salt, and pepper. Reduce heat and let stew simmer for 20 minutes.

Mix baking mix and milk for dumplings together to form a sticky dough. Drop by spoonfuls into stew. Cook, uncovered, for 10 minutes. Cover and continue to cook until dumplings are set, about 10 minutes more. Serve stew with a garnish of crumbled bacon.