Preheat the oven to 375 degrees F (190 degrees C). Spray a 4-quart rectangular baking dish with nonstick spray. Combine mozzarella and Italian blend cheeses in a bowl and place in the refrigerator.
Bring a large pot of lightly salted water to a boil. Add ziti and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain.
At the same time, heat 3 tablespoons oil in a Dutch oven over medium-high heat. Add sausage and break up into morsels. Sprinkle baking soda onto sausage, then add onion and garlic. Cook and stir, continuing to break up any clumps as it cooks, until browned and crumbly, 5 to 7 minutes. Pour off and discard any grease.
Add pasta sauce, olives, fennel seeds, Italian seasoning, anchovy paste, black pepper, and red pepper flakes. Add up to 3 tablespoons more oil if desired, and continue stirring until mixture comes to a boil. Reduce heat and simmer, stirring regularly, until thickened, 5 to 10 minutes. Remove from the heat and stir in ziti.
Spread 1/2 of the sauced ziti into the prepared baking dish and sprinkle 1/2 of the shredded cheese mixture evenly on top. Spoon or ladle the rest of the ziti evenly on top without disturbing the layers underneath; it's okay to have some ziti partially exposed as they will brown handsomely and deliciously as they bake. Sprinkle remaining shredded cheese mixture on top and sprinkle Parmesan across the surface.
Bake, uncovered, in the preheated oven until bubbly, 20 to 25 minutes. Remove from the oven and let rest for 15 minutes before serving.