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 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, 1 cup 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.
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