Preheat your oven to 350°F and lightly grease a 9x13 inch baking dish. While the oven heats, bring a large pot of salted water to a boil and cook the spaghetti according to package directions until al dente. Drain the pasta in a colander but don't rinse it—the starch helps bind the sauce.
In a large bowl, combine the room-temperature cream cheese, cottage cheese, and sour cream. I like to start by breaking up the cream cheese with a fork, then folding it together with the other ingredients until mostly smooth—a few small lumps are fine and will melt during baking. Stir in the garlic powder and Italian seasoning to distribute the flavors evenly.
Add the cooked spaghetti from Step 1 to the cheese sauce from Step 2 and toss gently until every strand is well coated. Transfer this mixture to your prepared baking dish and spread it into an even layer, creating a base for the chicken and alfredo layers.
Distribute the shredded chicken evenly over the pasta mixture, breaking up any clumps so it's scattered throughout rather than in one dense layer. Pour the alfredo sauce over the chicken, using a spatula or the back of a spoon to gently spread it so it reaches into the pasta beneath. I always make sure the sauce covers most of the surface to keep the top from drying out.
Sprinkle the freshly grated parmesan evenly over the alfredo layer, then top with the mozzarella, making sure to cover the whole surface. Bake in the preheated 350°F oven for 35 to 45 minutes, until the cheese is melted and bubbly around the edges and the top is lightly golden. The bake time may vary depending on your oven, so start checking around 35 minutes.