Wild Rice and Mushroom Soup

1/4 ounce dried, shiitake mushrooms, rinsed 4 1/4 cups, water 1 sprig, fresh thyme 1 , bay leaf 1 , garlic clove, peeled, plus 4 cloves, minced , Salt and pepper 1/4 teaspoons, baking soda 1 cup, wild rice 4 tablespoons, unsalted butter 1 pound, cremini mushrooms, trimmed and sliced 1/4 inch thick 1 , onion, chopped fine 1 teaspoon, tomato paste 2/3 cup, dry sherry 4 cups, low-sodium chicken broth or vegetable broth 1 tablespoon, soy sauce 1/4 cup, cornstarch 1/2 cup, heavy cream 1/4 cup, minced fresh chives 1/4 teaspoon, finely grated lemon zest