Preheat the oven to 350°F (177°C). Grease three 6-inch or two 8-inch cake pans with baking spray and line the bottoms with parchment paper rounds.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on high speed until creamy, about 2 minutes. Add the sugar and cream together on medium-high until light and fluffy, about 2 minutes, scraping the bowl and paddle halfway. Reduce speed to low and add the egg whites one at a time, mixing until just combined, scraping as needed. Add the oil and vanilla, then increase speed to high and beat for 1 minute.

Turn off the mixer and add the flour mixture all at once. Mix on low until just combined, then slowly pour in the buttermilk. Continue mixing on low for about 30 seconds, until the batter is smooth and slightly thin.

Divide the batter evenly among the prepared pans. Bake for 28 to 32 minutes, until the cakes spring back when lightly touched and a toothpick inserted in the center comes out clean or with a few moist crumbs. Let cool in the pans for 5 minutes, then transfer to a wire rack to cool completely.

In a small bowl, stir together the berry jam and water. Set aside.

In a medium bowl, combine the strawberries, blueberries, and raspberries. Toss with the lemon juice and zest. Set aside.

In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the mascarpone and cream cheese on medium speed until smooth, about 30 seconds. Gradually add the powdered sugar, a few spoonfuls at a time, beating on low until combined. Once all sugar is added, scrape the bowl, increase speed to medium, and beat until fluffy, about 30 seconds.

In another large bowl, combine the heavy cream, vanilla, and almond extract. Beat on medium speed until stiff peaks form, about 2 minutes. Gently fold the whipped cream into the mascarpone mixture until no streaks remain.

Once the cake layers are completely cool, level them if desired. Spread a small amount of frosting on a cardboard cake round, then place the first layer on top. Spread half of the jam mixture over the cake, then add a layer of Chantilly cream frosting. Press half of the lemon-coated berries into the frosting. Repeat with the next layer, using the remaining jam, frosting, and berries. Apply a thin crumb coat of frosting all over the cake, then refrigerate for at least 30 minutes to set.

Frost the cake with the remaining Chantilly cream frosting. For the decorative look, use a small spatula to create diagonal swipes on the sides. Garnish the top with a crescent of fresh berries.