Place potatoes into a large pot and cover with lightly salted water; bring to a boil. Reduce heat to medium-low and simmer until just tender, about 10 minutes. Drain and cool until easily handled, 5 to 10 minutes.
Peel potatoes and cut into 1/4-inch thick slices. Place in a large bowl. Sprinkle with salt. Add white wine, olive oil, and lemon juice; toss lightly to combine.
Mix mayonnaise and pesto together in a small bowl. Pour over potato salad and toss gently. Garnish with red onion. Chill until serving.