Heat the oven to 375°F. Line a rimmed baking sheet with parchment paper. In a large bowl, combine the breadcrumbs and 1/4 cup milk. Let them sit for 2 minutes so the breadcrumbs soften.
Add the ground turkey, egg, grated onion, 2 tablespoons of the ketchup, Worcestershire sauce, salt, and black pepper. Mix gently until just combined. Shape the mixture into a loaf on the prepared baking sheet, then spread the remaining ketchup over the top.
Bake the meatloaf until cooked through and the center reaches 165°F, about 45 to 55 minutes. Let it rest for 10 minutes before slicing.
While the meatloaf bakes, put the potatoes in a large saucepan and cover them with cold water. Bring to a boil, then reduce the heat and simmer until the potatoes are tender when pierced with a fork, about 15 to 20 minutes. Drain well.
Return the potatoes to the saucepan. Add the butter and warm milk, then mash until creamy. Cover to keep warm while you cook the green beans.
Heat the olive oil in a large skillet over medium heat. Add the green beans and cook, stirring occasionally, until bright green and tender-crisp, about 7 to 9 minutes.
Slice the rested meatloaf and serve it with the mashed potatoes and green beans.