Place water, onion, soy sauce, soy-based liquid seasoning, garlic, and ginger root in a saucepan; bring to a boil.
Mix cornstarch with 2 tablespoons boiling water. Add to the saucepan. Add mushrooms and bouillon. Reduce heat to medium-high; simmer until flavors are blended, about 7 minutes. Add tofu and watercress. Simmer soup for 2 minutes more.
Pour in eggs slowly, whisking constantly, until cooked, 1 to 2 minutes.