Line an 8×8 inch square baking pan with parchment paper, leaving some overhang for easy lifting.

In a medium bowl, combine the almond flour, melted butter, 3 tablespoons sugar-free powdered sweetener, 1/2 teaspoon vanilla bean paste, and salt, and mix until a crumbly dough forms.

Transfer the crust mixture to the prepared pan and press it firmly and evenly into the bottom of the pan, pushing it into the corners to form a compact layer.

Place the pan with the crust in the refrigerator to chill while you prepare the cheesecake filling.

In a large mixing bowl, beat the softened cream cheese with a hand mixer on medium speed for 1 to 2 minutes until completely smooth and lump-free.

Add 3/4 cup sugar-free powdered sweetener to the cream cheese and beat again until light and fluffy, scraping down the sides of the bowl as needed.

Add the sour cream, 1 teaspoon vanilla bean paste, and lime juice to the bowl and mix on low speed just until the filling looks smooth, thick, and glossy.

Remove the chilled crust from the refrigerator and pour the cheesecake filling over it, spreading it into an even layer with a spatula and smoothing the top.

Tap the pan gently on the counter a few times to release any air bubbles from the filling.

Cover the pan tightly with plastic wrap or foil and refrigerate for at least 4 hours, or until the cheesecake is fully set in the center.

Just before serving, combine the mixed berries and 1 tablespoon sugar-free sweetener in a small bowl, stir, and let sit for 10 to 15 minutes to create a light syrup.

Lift the cheesecake slab out of the pan using the parchment, place it on a cutting board, and cut into 16 squares with a sharp knife, wiping the blade clean between cuts.

Spoon the macerated berries over the cheesecake bars just before serving or serve on the side.