In a large pot, heat the coconut oil over medium heat. Add the diced sweet onion and cook until translucent, about 3-4 minutes. Then, stir in the minced garlic and freshly grated ginger, cooking for an additional minute until fragrant.
Next, toss in the sliced red bell pepper, baby carrots, and sugar snap peas. Sauté the vegetables for about 5 minutes, allowing them to soften slightly while still retaining some crunch.
Add the red curry paste to the pot, stirring well to coat the vegetables. Cook for another 1-2 minutes to enhance the flavor.
Pour in the slow-sodium chicken stock and the can of coconut milk. Stir everything together, bringing the mixture to a gentle simmer.
Once the soup is simmering, add the cooked and shredded chicken breast. Allow the soup to heat through for about 5 minutes, letting all the flavors meld together.
Finally, stir in the spiralized zucchini. Cook for an additional 2-3 minutes, just until the zoodles are tender but not mushy.
Remove the soup from heat and ladle it into bowls. Top each serving with fresh chopped cilantro and sliced green onions. Serve with lime wedges on the side for spritzing over the soup just before enjoying.