In a large, non-reactive bowl, combine tomatoes, 2 tablespoons olive oil, minced garlic, ¼ teaspoon salt, and pepper. Stir to combine; set aside.
Bring a large pot of water to boil, then add the pasta. Cook until al dente, following package directions. Drain and return the pasta to the now-empty pot.
Meanwhile, heat remaining 3 tablespoons of oil in a large skillet with a lid over medium-low heat. Add the zucchini, sliced garlic, crushed red pepper, and remaining ¼ teaspoon salt. Cook, covered and stirred occasionally, for 10–15 minutes, until zucchini breaks down. Depending on how tender the zucchini is, an immersion blender may be helpful to coarsely chop the zucchini if it is not fully soft and creamy after 15 minutes.
Add the water to the skillet, cover, and turn the heat to medium-high to bring the water to a simmer. Add the sugar snap peas and cover to cook for 2–4 minutes, just until pods are crisp-tender.
Add vegetables, half of the basil, and lemon juice to the pasta and stir gently to combine. Transfer to a large, shallow serving bowl and sprinkle evenly with ¼ cup pecorino. Arrange tomatoes and their juice across the top, then scatter remaining basil across the top. Serve warm, passing extra pecorino at the table.