Preheat the oven to 350°F. Line the bottom of a 7-inch springform pan with parchment paper and butter the sides and bottom.
Toss ½ cup blueberries with 1 teaspoon flour (taken from the measured flour) and set aside. In a small bowl, whisk together the flour, baking powder, baking soda, and salt and set aside.
In a large bowl, beat the butter and sugar until light and fluffy, about 2–3 minutes. Add the egg and beat until incorporated. Mix in the vanilla, Greek yogurt, and lemon zest until smooth.
Add the flour mixture gradually and mix on low speed just until combined. Do not overmix. Gently fold blueberries into the batter.
Transfer the batter to the prepared pan and smooth the top evenly. Arrange the apricot slices decoratively over the batter, slightly overlapping them if desired. Scatter the remaining ¼ cup blueberries among the apricot slices.
Bake for 50–60 minutes, or until the cake is golden and a toothpick inserted into the center comes out clean. If the top begins browning too quickly, loosely tent with foil after about 40–45 minutes. Let the cake cool in the pan for 15–20 minutes.