Preheat the oven to 375°F (190°C).
Heat the large skillet over medium-high and add the olive oil.
Add the chopped onion and chopped sweet potato; cook until they begin to caramelize, about 5 minutes.
Add the minced garlic and cook 30 seconds until fragrant.
Add the ground turkey (or chicken) and cook, breaking it up, until no longer pink, about 8–10 minutes.
Stir in the chipotle chile powder, cumin, and a generous pinch each of kosher salt and black pepper.
Add 1/2 cup water to the skillet and cook, stirring occasionally, until the water evaporates and the mixture is slightly saucy.
Remove the skillet from the heat and stir in the chopped cilantro, chopped green chiles, and drained black beans.
Arrange tortilla chips in a single layer on a large baking sheet. Sprinkle half of both cheeses (or half of the combined cheese) over the chips.
Spoon the turkey and bean mixture evenly over the chips, then sprinkle the remaining cheeses on top.
Bake in the preheated oven until the cheese is melted and bubbly, 10–15 minutes.
While nachos bake, make the jalapeño yogurt: in a small bowl combine the plain Greek yogurt, seeded chopped jalapeño, lime juice, and a pinch of kosher salt; taste and adjust salt as needed.
Top the baked nachos with diced mango, additional cilantro, and dollops of the jalapeño yogurt; serve with jalapeños and lime wedges as desired.