Preheat the oven to 425°F (220°C). Lightly spray a large sheet pan with cooking spray.
Beat the eggs in a large bowl until smooth. Add the refrigerated tortellini and toss to coat evenly with the egg.
In a gallon zip-top bag combine the Italian seasoned bread crumbs, grated Parmesan, garlic powder, and salt; seal and shake to mix.
Add the egg-coated tortellini to the bag in batches if needed, seal, and shake until each piece is evenly coated with the breadcrumb mixture.
Arrange the coated tortellini in a single layer on the prepared sheet pan and lightly spray the tops with cooking spray.
Bake for 10 minutes, then use a spatula to flip each tortellini and bake an additional 8–10 minutes until the edges are golden and toasted.
Heat the marinara, Alfredo, and pesto sauces according to package instructions and transfer to small bowls for dipping.
Serve the toasted tortellini immediately with the warmed sauces for dipping.