Japanese bread is soft for a reason: most of it contains milk, butter or egg. Bakery items usually have no label at all. Sliced bread (食パン) and soft rolls almost always contain milk or butter, often egg. Bakeries sell pastries unwrapped: nothing to read, and staff may not know every ingredient. Packaged bread at the konbini has a label. Check 乳成分, 卵 and バター. Crusty “hard” breads (ハード系) are often simpler, but ask anyway.