For the Chicken Stock: In a large soup pot or Dutch oven, combine chicken, water, celery, carrots, leek, salt, and thyme sprigs. Bring to a simmer over medium-high heat. Reduce heat to medium and simmer, adjusting head as needed to maintain gentle simmer, until chicken is cooked through and tender, about 40 minutes.

Using tongs, carefully remove chicken from pot and transfer to a medium bowl. Let chicken sit until cool enough to handle, about 5 minutes. Discard skin and finely shred meat. Set shredded meat aside and return bones to pot with stock. Continue to simmer until stock is flavorful and rich, 30 to 40 minutes.

Using a fine-mesh strainer, strain stock into a heatproof bowl or large measuring cup. Wipe pot dry. Discard solids and use a ladle or large spoon to skim off any fat on surface of the stock. Set aside.

For the Soup: In the now-empty large soup pot or Dutch oven, melt butter over medium heat. Add celery, carrots, fennel, salt, and pepper and cook, stirring often, until vegetables are softened, about 8 minutes. Stir in garlic and thyme and cook until fragrant, about 1 minute.

Sprinkle flour over vegetables; cook, stirring frequently, until evenly coated and flour begins to stick to bottom, about 2 minutes.

Slowly pour in the reserved chicken stock, whisking until the flour is fully incorporated. Stir in the rice and baking soda, if using, and bring to a boil over medium-high heat. Reduce heat to medium-low, and simmer until flavors meld and wild rice has split open and is tender but still retains a bit of chew, 40 to 50 minutes. Return shredded chicken to soup and simmer until heated through, about 2 minutes. Remove from heat, and stir in heavy cream, lemon zest, and lemon juice.

Divide soup evenly among serving bowls and top with reserved celery leaves.