Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente. Reserve about 1/2 cup of the pasta water, then drain the pasta and set aside.
Heat olive oil in a large skillet over medium heat. Add the diced onion and bell pepper, cooking until softened, about 4-5 minutes. Stir in the minced garlic and cook for an additional 30 seconds, until fragrant.
Sprinkle in the Cajun seasoning and cayenne pepper, stirring to coat the vegetables. Add the crawfish tails and cook just until they turn opaque and warm through, about 3-4 minutes.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a gentle simmer, letting it thicken slightly, roughly 5 minutes. Add the cherry tomatoes and season with salt and pepper to taste.
Add the cooked linguine to the skillet, tossing to coat the pasta evenly with the spicy cream sauce. If the sauce seems too thick, add reserved pasta water a tablespoon at a time until you reach the desired consistency.
Remove from heat and sprinkle the dish with chopped green onions. Serve immediately for the best texture and flavor.