Synthesize the Pesto: In a food processor, combine the ¼ cup toasted pine nuts, nutritional yeast, lemon juice, garlic, and ⅛ teaspoon salt. Pulse to a coarse texture. Add basil; pulse until finely chopped. With the motor running, stream in olive oil until smooth. Scrape down the sides and set aside.
Prepare the Whole-Grain Pasta: Bring a large stockpot of water to a rolling boil. Do not salt the water. Add the whole wheat pasta and cook according to package directions until al dente. Before draining, reserve at least ½ cup starchy pasta water.
Cool and Lock Hydration: Drain the pasta in a colander. Spread the hot pasta in a single layer on a baking sheet. Let the pasta and the reserved pasta water cool to room temperature, about 15 minutes.
Prime the Vegetables: While the pasta cools, slice the zucchini and yellow squash into very thin rounds with a mandoline or sharp knife. Halve the cherry tomatoes. Rinse and drain the chickpeas thoroughly.
Unify the Ingredients: In a large mixing bowl, combine the cooled pasta, zucchini, squash, tomatoes, and chickpeas. Pour the pesto over the top.
Emulsify and Season: Toss gently. Drizzle in half of the cooled reserved pasta water to help the pesto coat every ingredient. Add the 2 tablespoons lemon juice, ⅛ teaspoon salt, and black pepper to taste. Continue tossing, adding more pasta water a tablespoon at a time, until the salad reaches your desired consistency.
Garnish and Serve: Transfer to a serving platter. Garnish with 2 tablespoons toasted pine nuts, torn basil leaves, and a pinch of red pepper flakes, if desired. Serve immediately at room temperature.