Dice the onion, celery, and carrots into even 1/4-inch pieces, mince the garlic, and cut the potatoes into 1/2-inch cubes (keep them in cold water until needed). Chop the bacon, measure the dry seasonings, and prep the corn, cream, cheddar, and green onions.
Cook the chopped bacon in a large Dutch oven over medium heat for 8 to 10 minutes until browned and crisp. Move it to a paper towel-lined plate and leave about 2 tablespoons of drippings in the pot.
Melt the butter into the bacon drippings, then add the onion, celery, and carrots. Cook for 6 to 8 minutes until the onion is soft and translucent, then stir in the garlic for 30 to 60 seconds until fragrant.
Sprinkle the flour evenly over the vegetables and stir constantly for 1 to 2 minutes until no dry patches remain and the mixture smells lightly toasty.
Pour in the broth about 1 cup at a time, whisking well after each addition and scraping up the browned bits. Stir in the thyme, smoked paprika, bay leaf, salt, and pepper, then add the drained potatoes and nestle in the chicken breasts.
Bring to a gentle boil, then reduce the heat to medium-low. Partially cover and simmer for 20 to 25 minutes, stirring occasionally, until the potatoes are fork-tender and the chicken reaches 165°F.
Move the chicken to a cutting board, rest for 5 minutes, and shred with two forks. Discard the bay leaf.
Reduce the heat to low and stir in the frozen corn, cream-style corn, and heavy cream. Return the shredded chicken and half the bacon to the pot and heat gently for 5 to 8 minutes without boiling. Season to taste.
Ladle into warm bowls and top each with shredded cheddar, the remaining crispy bacon, and sliced green onions. Serve right away.