Set aside broth and chopped chicken if you made them fresh for this recipe.
Over medium high heat, heat extra big sauté pan, low pot or Dutch oven style pan. Add olive oil, and sauté onion, whites of green onions and 1/2 teaspoon sea salt. If using mushrooms, wait to add them. For celery, add it with the onions. Cook, stirring occasionally, 15 minutes, over medium heat, reducing heat as needed (after 5 to 10 minutes), so veggies don't get too dark. Add mushrooms after 10 minutes, if using.
After 15 minutes, stir in optional onion and garlic powders, plus dried herbs and dried ginger powder. Sauté 2 minutes until fragrant. Add fresh garlic, and stir until mixed in.
While the veggies cook, heat a large pot of water, and cook pasta according to package instructions. Cook pasta one minute shy of done, so it is truly al dente (this is 9 to 10 minutes for cassava pasta). Strain, and set aside. (At this point, the cooking can pause if you'd like to wait to finish the recipe. This can be the "Meal Prep" part of the meal, to do early.)
Shortly before you're ready to serve: Measure 1 cup coconut milk into larger measuring cup or small mixing bowl -- or for dairy version: 1/2 cup heavy cream + 1/2 cup broth. Add to it and whisk in: tapioca flour and optional Dijon mustard.
If you turned the heat off under the veggies, return the heat to Medium. Add 2 cups of the overall chicken broth (and optional peas, if you're using).
When the veggies and portion of broth begin to simmer, freshly whisk the creamy tapioca slurry, and pour it in all at once. Use whisk to move the veggies and cream around until they're well mixed. Add final 2 cups chicken broth. Whisking, bring to a simmer again. The soup will thicken. Simmer slowly while whisking 1 to 2 minutes.
Add chicken, pasta, greens of green onions and fresh lemon juice. Heat until very hot, stirring gently (so as not to break up pasta too much). Once heated through, sprinkle in most but not all of the fresh thyme. Serve, topped with the last of the fresh thyme.
NOTE: Chicken Tetrazzini Soup is very thick (and satisfying!). If it sits for a few hours, it will thicken. If you want leftovers thinner, it's fine to add an additional 2 cups of broth.