Line a 9-inch square metal pan with two crossed sheets of parchment, leaving enough overhang to lift out the finished bars. Combine the graham cracker crumbs and 25 grams granulated sugar in a bowl, then stir in the melted butter until every crumb looks evenly moistened. Press the mixture firmly across the bottom of the pan using a flat measuring cup. Compact the corners especially well, then refrigerate the crust for 30 minutes while preparing the filling.
Sprinkle the gelatin over the cold water in a small bowl and leave it undisturbed for 5 minutes. Meanwhile, combine the quartered strawberries, 100 grams granulated sugar and lemon juice in a medium saucepan. Puree with an immersion blender, then simmer over medium heat for 12 to 15 minutes, stirring frequently, until the mixture weighs 340 grams and looks glossy and slightly thickened. Remove from the heat, whisk in the bloomed gelatin until dissolved, and cool for 25 to 30 minutes until fluid but no longer warm.
Pour the cold heavy cream into a clean medium bowl. Using an electric mixer with the whisk attachment, beat on medium speed until the cream thickens, then increase to medium-high and continue just until medium peaks form, about 2 to 3 minutes total. The lifted whisk should leave a peak with a gently bent tip. Stop before the cream looks grainy or stiff, since slightly flexible whipped cream folds into the cheesecake base without losing excessive volume.
In a large bowl, beat the room-temperature cream cheese, confectioners’ sugar, vanilla and salt on medium speed for 2 minutes, scraping the bowl and beaters halfway through, until completely smooth. With the mixer on low, gradually add the cooled strawberry mixture and blend until the color is uniform with no pale cream cheese streaks. Fold one-third of the whipped cream into the base to loosen it, then gently fold in the remainder until evenly combined and airy.
Scrape the strawberry cheesecake filling onto the chilled crust and spread it into an even layer with an offset spatula, pushing the mixture into each corner without disturbing the crumbs. Smooth the top, tap the pan lightly on the counter twice to release large air pockets, and cover without touching the surface. Refrigerate on a level shelf for at least 6 hours or overnight. The center is set when it remains still as the pan is nudged and feels firm under light fingertip pressure.
Use the parchment overhang to lift the cold cheesecake slab onto a cutting board. Arrange the thoroughly dried sliced strawberries over the surface just before serving. Warm a large chef’s knife under hot water, wipe it completely dry, and cut the slab into 16 squares, cleaning and reheating the blade between cuts. If the first cut drags through the filling, return the slab to the refrigerator for 30 minutes before continuing. Keep the finished bars chilled until serving.