Heat oven to 425°F. Line a sheet pan with foil and set a wire rack on top. Brush the rack lightly with oil.
Stir breadcrumbs and Greek yogurt in a large bowl. Let stand 3 minutes to hydrate.
Add red onion, garlic, parsley, mint, oregano, lemon zest, lemon juice, salt, pepper, and cumin. Mix to combine.
Add turkey and feta. Gently mix with a fork or hands until just combined; do not overwork.
Scoop tablespoonfuls and roll into 1½-inch meatballs. Arrange on the prepared rack and brush tops with olive oil.
Bake 14–16 minutes until centers reach 165°F. Broil 1–2 minutes to brown, then rest 5 minutes.
Serve warm with tzatziki and extra lemon if desired.