Preheat the oven to 350 degrees . In a large skillet, cook the bacon over medium heat until crisp. Transfer to paper towels to drain; pour the rendered fat into a small, heatproof bowl. Add the green beans and 1/4 cup water to the skillet and simmer over medium-high heat until the water evaporates, 2 to 3 minutes; season with salt. Transfer to an ovenproof glass bowl.
In the skillet, heat 1-1/2 teaspoons of the bacon fat. Add the squash and cook over medium-high heat until light brown; season with salt and pepper. Spoon the squash over the green beans. Add 1-1/2 teaspoons more of the bacon fat and the tomatoes to the skillet and cook for 2 minutes; spoon over the squash. Add another 1-1/2 teaspoons of the bacon fat and the white beans to the skillet and heat through; season with pepper and spoon over the tomato layer. Bake the vegetables until warmed through, 10 minutes.
Meanwhile, toast the bread. Top the baked vegetable bowl with layers of the lettuce and cheddar. Top with the yogurt, then crumble the bacon and sprinkle on top. Serve with the toast.