Preheat the oven to 350F (175C). Line the bottom of a springform pan with parchment paper and lightly grease the sides.
Beat the eggs and sugar on high speed for about 5 minutes until thick and pale. Stir in the vegetable oil.
Whisk together the flour and baking powder separately.
Add half of the flour mixture to the egg mixture, mixing on low speed just until combined.
Stir in the lemon zest and vanilla extract.
Add the seltzer water, mixing until incorporated.
Add the remaining flour mixture and mix until smooth.
Pour the batter into the prepared pan. Arrange the mixed berries over the top.
For the crumb topping, combine flour, sugar, and sea salt. Rub in softened butter until large crumbs form.
Sprinkle the crumb topping evenly over the berry-topped batter.
Bake for about 45 minutes or until golden brown and a toothpick comes out clean.