Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until tender yet firm to the bite, about 12 minutes. Drain.
Heat olive oil in a large pot over medium-high heat. Add red onion, garlic, and garlic scape; cook, stirring occasionally, until fragrant, about 2 minutes. Squeeze tomatoes into the pot. Add sweet pepper, broccoli, and baby bella mushrooms. Simmer until flavors combine, about 5 minutes.
Stir tomato paste, white sugar, basil, Italian seasoning, red pepper flakes, cinnamon, and salt into the pot. Reduce heat to medium-low; cook until broccoli is tender. Add chicken strips; simmer sauce for 20 minutes.
Stir rigatoni into sauce. Mix in Parmesan cheese, mozzarella cheese, and feta cheese.