The mushroom listed by Wikipedia as a vegetable used in tempura is shiitake.
Shiitake mushrooms are commonly used in vegetable tempura, where their firm texture and savory flavor stand up well to a thin, crisp batter. They may be fried whole or in large pieces, usually with the stem trimmed, and served with tentsuyu dipping sauce or seasoned salt.
Shiitake, or Lentinula edodes, is native to East Asia and has long been cultivated and eaten in Japan, China, and neighboring regions. Fresh mushrooms provide a meaty texture, while dried shiitake are prized for their concentrated flavor and are especially important in soups, simmered dishes, and vegetarian dashi.
The other options are also edible Japanese mushrooms, but they are not the mushroom named in the standard Wikipedia tempura ingredient list. Tempura’s vegetable category is broad: it can include roots, peppers, squash, eggplant, leafy herbs, and several kinds of mushrooms.