Line the bottom and sides of a 9-inch springform pan with a strip of parchment (or wrap the outside with foil). Combine the cracker crumbs, 1/2 cup sugar and lemon zest in a medium bowl. Stir in the melted butter until the mixture feels like damp sand.
Press the crumb mixture firmly into the bottom of the prepared pan and about 1/2 inch up the sides using the bottom of a measuring cup for even compaction. Chill the crust in the refrigerator while you make the filling (about 10 minutes).
In a large mixing bowl, beat the room-temperature cream cheese with 1/3 cup sugar and the vanilla extract on medium speed until smooth and lump-free, about 2–3 minutes. Scrape down the bowl as needed.
Add the lemon juice to the cream cheese and mix until incorporated. In a separate chilled bowl, whip the heavy cream with the sifted powdered sugar to medium-stiff peaks — it should hold shape but still be silky.
Gently fold about one-third of the whipped cream into the cream cheese to lighten it, then fold in the remaining cream in two additions until the filling is uniform and airy. Avoid overmixing to keep the filling light.
Spoon the filling over the chilled crust and smooth the top with an offset spatula. Cover the surface directly with plastic wrap (touching the filling) and refrigerate the cake for at least 6 hours, preferably overnight, to firm up.
Make the blueberry compote while the cheesecake chills: whisk together the water and cornstarch in a small saucepan until dissolved. Add 1/3 cup sugar and the blueberries, then stir in the lemon juice and zest.
Cook the berries over medium heat, stirring occasionally, until the fruit releases juices and the sauce thickens slightly, about 5–8 minutes. Remove from heat and let the compote cool to room temperature, then chill in the fridge until ready to use.
When the cheesecake has fully set, release the springform ring and transfer the cake to a serving plate. Spoon the cooled blueberry compote over the top (reserve a little for serving on the side). Slice with a hot, clean knife for neat pieces.