Place tofu on several paper towels and sprinkle with 1/4 teaspoon salt. Turn tofu over, sprinkle with the remaining 1/4 teaspoon salt, place more paper towels on top and weight the tofu down with a plate. Set aside for 5 minutes. Cut the tofu into roughly 1-inch cubes.
Heat a 14-inch flat-bottomed wok or large skillet over high heat until a bead of water vaporizes within 1 to 2 seconds of contact. Swirl in 1 tablespoon oil; add garlic and scallions and stir-fry until fragrant, 10 seconds. Add mushrooms and stir-fry until just beginning to soften, 1 minute. Transfer to a plate.
Swirl the remaining 1 tablespoon oil into the pan, reduce the heat to medium, add the tofu and pan-fry, turning midway through cooking, until it begins to brown, about 3 minutes. Swirl in Sichuan Sauce and the mushroom mixture; increase the heat to high and stir-fry until the tofu is just heated through and the sauce clings to it, 30 seconds to 1 minute. Discard the garlic. Serve immediately.
Chinkiang is a dark, slightly sweet vinegar with a smoky flavor. It is available in many Asian specialty markets. If unavailable, balsamic vinegar is an acceptable substitute.