Butter is the bridge between bread and pastry. In small amounts, it softens. In large amounts (like Brioche), it transforms the dough into a foam-like structure that is more air than wheat.

Sourdough is traditionally lean (Flour, Water, Salt). When you introduce a lipid like Extra Virgin Olive Oil, you are entering the territory of "Enriched Dough." You are trading some crust crispness for crumb tenderness.