Preheat oven to 350°F. Grease a 9x5-inch loaf pan and line with a parchment sling.
Grate zucchini, then squeeze out moisture in a clean towel until very dry.
Mash bananas in a large bowl until mostly smooth.
Whisk in oil, eggs, vanilla, and yogurt until blended.
In another bowl, whisk flour, sugars, baking soda, baking powder, salt, cinnamon, and nutmeg.
Stir dry ingredients into wet just until a few streaks remain.
Fold in zucchini and walnuts until evenly distributed; do not overmix.
Scrape batter into the prepared pan and smooth the top.
Bake 50–60 minutes until a tester comes out clean. Tent with foil if browning fast.
Cool in pan 10 minutes, then lift out and cool completely before slicing.