Heat the canola oil in a large Dutch oven over medium heat, then season the chicken thighs generously with Cajun seasoning. Add the chicken and sear for about 3 minutes per side until deeply browned, then remove and set aside.
Add the andouille sausage to the same pot and cook until lightly caramelized, then stir in the browning or roux and cook for about 5 minutes, stirring often to develop deep color and flavor without burning.
Remove the sausage, then add the celery, onion, and bell pepper, cooking for about 3 minutes while scraping up the browned bits from the bottom until the vegetables soften and the onions turn translucent.
Stir in the garlic, hot sauce, bay leaf, cayenne, and thyme, cooking for 2–3 minutes until fragrant and well combined.
Add the rice and stir to coat evenly, then return the chicken and sausage to the pot along with the Worcestershire sauce and chicken stock. Bring to a boil, cover, and reduce to a low simmer.
Cook for 25–30 minutes until the liquid is absorbed and small steam holes form on the surface, then gently fluff with a fork and stir in half of the green onions.
Cover and cook for an additional 10 minutes, then taste and adjust seasoning as needed before garnishing with the remaining green onions and serving hot.