Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes; drain.
While pasta boils, process grape tomatoes, Parmesan cheese, garlic scapes, olive oil, basil leaves, sun-dried tomatoes, and lemon juice in a food processor until smooth; season with salt and pepper.
Prepare a large skillet with cooking spray and place over medium heat. Cook spinach leaves in hot skillet until slightly wilted, about 3 minutes; add drained linguine and pesto sauce. Cook and stir to coat linguine is sauce and until everything is hot, 2 to 3 minutes.
