Add raspberries, sugar, and ½ cup water to a saucepan over medium heat.
Stir to dissolve the sugar, then simmer until raspberries are broken down, about 3 minutes. Remove from heat.
Mash the berries with a potato masher or fork, then strain through a fine mesh strainer to remove seeds. Set aside and let the raspberry juice cool completely.
Preheat the oven to 375 F.
Make the crust: Add the graham cracker crumbs, sugar, cinnamon, and melted butter to a bowl and stir to combine well.
Press the crust mixture into a pie pan, then bake for 8 minutes or until just browned. Set aside to cool.
Make the filling: Mix together the sweetened condensed milk, sour cream, key lime juice, cooled raspberry juice, and lime zest in a bowl.
Pour into the cooled graham cracker crust and smooth across the top. Bake for 15-20 minutes, until just set.
Let the pie cool completely at room temperature, then chill for 1 hour.
While the pie is chilling, make the topping. Add all the berries, sugar, and ¼ cup water to a saucepan over medium heat.
Stir to dissolve the sugar, then bring to a simmer.
Stir cornstarch together with ¼ cup water, then add to the skillet and stir to dissolve. Let the berries thicken into a compote, then remove from the heat and cool completely.
To serve, spoon the compote over the cooled and chilled pie.