Bring a large pot of salted water to a boil. Add the whole wheat spaghetti and cook according to package instructions until al dente, usually around 8-10 minutes. Drain and set aside, reserving about 1/2 cup of pasta water for later.
In a mixing bowl, whisk together the creamy peanut butter, soy sauce, honey, sriracha sauce, and lime juice until smooth and well combined. If the sauce feels too thick, add a splash of warm water to thin it out slightly. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Season the sliced chicken breast with salt and pepper. Add the chicken to the skillet and cook for 5-7 minutes, stirring occasionally, until cooked through and lightly browned. Remove the chicken from the pan and set aside.
In the same skillet, add the minced garlic, sliced red bell pepper, snap peas, and chopped green onions. Sauté for 3-4 minutes until the vegetables are tender-crisp and fragrant.
Return the cooked chicken to the skillet with the vegetables. Pour the peanut sauce over the mixture and toss to coat evenly. Add the cooked spaghetti and gently toss again to combine all the ingredients. If the sauce is too thick, add a little reserved pasta water a tablespoon at a time until you reach your desired consistency.
Remove from heat and sprinkle chopped cilantro over the top for a fresh, herbal note. Serve immediately, enjoying the perfect blend of spicy, sweet, and savory flavors.