Whisk bean sauce, vinegar, sweet chile sauce, lemongrass, 1 tablespoon soy sauce, lemon juice, spicy chile sauce, minced ginger, and sliced ginger together in a bowl until dressing is well combined.
Bring a large pot of lightly salted water to a boil. Cook soba noodles in boiling water, stirring occasionally, until noodles are tender yet firm to the bite, 10 to 12 minutes. Drain.
Heat 2 tablespoons oil in a wok or large skillet over medium-high heat; add garlic scapes and cook until tender, 2 to 3 minutes. Add radishes, turnip greens, snap peas, and 1 tablespoon soy sauce; sprinkle sugar over top. Cook and stir mixture until radish is tender and turnip greens are wilted, 5 to 10 minutes.
Mix dressing and soba noodles into garlic scape mixture.
Heat 1 teaspoon oil in a separate skillet over medium heat; cook and stir chard until it starts to wilt, 1 to 2 minutes. Remove skillet from heat and divide chard between 2 plates. Top chard with noodle mixture and add sesame seeds.