Trim and cut 2 medium summer squash and 2 medium zucchini crosswise into 1/4-inch-thick rounds. Transfer to a colander set in the sink. Sprinkle with 1 teaspoon kosher salt and toss to coat. Let sit for 10 to 15 minutes to allow some moisture to release. Meanwhile, heat air fryer to 400℉.
Transfer the squash to a paper towel-lined baking sheet in a single layer. Thoroughly pat dry with more paper towels, then transfer to a bowl. Sprinkle with 1/2 teaspoon garlic powder, 1/2 teaspoon Italian seasoning, and 1/4 teaspoon black pepper. Drizzle with 1 tablespoon olive oil and toss to coat.
Transfer the rounds to air fryer basket. Air fry until golden at the edges, tossing the squash halfway through, 20 to 25 minutes total. Meanwhile, remove the leaves from 2 fresh basil sprigs and tear into pieces.
When the squash is ready, add about 2/3 of the basil to the basket and toss to coat. Taste the squash and season with kosher salt and black pepper as needed. Transfer to a medium serving bowl. Just before serving, finely grate the zest from 1/2 small lemon with a Microplane or the small holes of a box grater over the squash. Garnish with remaining basil leaves.