Position a rack in the center of the oven and heat it to 350°F. Lightly grease a 9-inch square metal pan that is at least 2 inches deep. Line the bottom and two opposite sides with parchment, leaving enough overhang to lift the chilled cheesecake out later. Set the lined pan on a rimmed baking sheet, which makes the filled pan easier to move without sloshing.
Combine the chopped strawberries, 50 g sugar, and lemon juice in a small saucepan. Stir over medium heat until the berries release their liquid and simmer, about 4 minutes. Mix 8 g cornstarch with 15 g cold water, stir it into the fruit, and cook for 1 to 2 minutes until glossy and thick enough to leave a brief trail across the pan. Transfer to a shallow bowl and cool to room temperature.
Combine the graham cracker crumbs, 25 g sugar, and 1/4 teaspoon salt in a medium bowl. Stir in the melted butter until every crumb looks evenly moistened and the mixture holds together when squeezed. Spread it in the lined pan and compact it into a level layer with the bottom of a measuring cup. Bake for 10 minutes, then place the pan on a rack. Reduce the oven temperature to 325°F.
Place the softened cream cheese in a large bowl or stand mixer fitted with the paddle. Beat on low speed for 1 to 2 minutes, scraping the bowl and paddle, until completely smooth. Mix the 150 g sugar, 12 g cornstarch, and 1/4 teaspoon salt together, then beat them into the cream cheese on low just until blended. Mix in the sour cream and vanilla. Add the eggs one at a time, mixing only until each yolk disappears.
Pour the cheesecake filling over the warm or cooled crust and smooth it level with an offset spatula. Spoon the cooled strawberry mixture over the surface in small, evenly spaced portions, reserving none. Draw a thin knife through the fruit and filling with a few shallow figure-eight motions. Stop while broad red ribbons remain visible; overmixing will muddy the color and distribute excess fruit moisture throughout the filling.
Bake the pan on the rimmed baking sheet at 325°F for 38 to 45 minutes. The outer 2 inches should look set and slightly puffed, while the center should wobble gently as one piece when the pan is nudged, not ripple like liquid. An instant-read thermometer inserted into a plain cheesecake area near the center should register about 150 to 155°F. Avoid baking until rigid because residual heat continues setting the eggs.
Turn off the oven, prop the door open several inches, and leave the cheesecake inside for 20 minutes to slow the temperature change. Transfer the pan to a wire rack and cool at room temperature for about 40 minutes, until it no longer feels warm. Cover the pan without touching the surface and refrigerate for at least 5 hours, preferably overnight. The filling must feel cold and firm before lifting or slicing.
Run a thin knife along the two unlined edges, then use the parchment overhang to lift the chilled slab onto a cutting board. For 16 bars, trim only visibly uneven edges if desired, then make four equal rows in each direction. Dip a thin-bladed knife in hot water, wipe it completely dry, and make one downward cut. Clean, warm, and dry the blade before every cut so strawberry and filling do not smear across the edges.