Heat the oven to 350 degrees F and grease an 8-inch square baking pan. Whisk the flour, 3/4 cup granulated sugar, baking powder, and salt together.
Whisk the oat milk, oil, egg, and 2 teaspoons vanilla extract in a separate bowl. Stir the wet mixture into the dry ingredients just until smooth.
Spread the batter in the prepared pan and bake for 24 to 28 minutes. Cool the cake completely, then cut it into 1-inch cubes.
Toss the mixed berries with 1/4 cup granulated sugar and lemon juice. Let them stand for 20 minutes so they become glossy and release some juice.
Whisk 2 cups oat milk, 1/3 cup granulated sugar, and cornstarch together in a saucepan. Cook over medium heat, whisking constantly, until thick and bubbling.
Remove the custard from the heat and stir in the vegan butter and 1 teaspoon vanilla extract. Cover the surface and refrigerate until cold.
Layer half of the cake cubes, berries and their juices, vanilla custard, and coconut whipped topping in a trifle bowl. Repeat each layer once more.
Refrigerate the trifle for at least 3 hours so the cake absorbs the berry juices and custard, then serve cold.