Bring a large pot of water to a boil. Add the beans and cook until tender, about 2 minutes. Using a slotted spoon, transfer the beans to a bowl of ice water. Drain and set aside. Add the noodles to the boiling water and cook according to the package directions.
Meanwhile, in a baking dish, combine 3 tablespoons of the soy sauce, the garlic, grated ginger, and 1 tablespoon of the wine. Rinse the salmon and pat it dry with paper towels. Add it to the baking dish and turn to coat. Scatter the sliced ginger and scallions over the top. Cover with foil and bake until the fish is the same color throughout and flakes easily, about 20 minutes.
Meanwhile, in a small saucepan over medium-high heat, combine the vinegar, lemon juice, sugar, and the remaining soy sauce and wine, stirring until the sugar dissolves. Bring to a boil and cook until reduced by half, about 3 minutes. Remove from heat and cover to keep warm. Divide the drained noodles and beans among individual plates, top each with a salmon fillet, and drizzle with the glaze.