For the everything-bagel strata: Combine the cream cheese and eggs in a blender and blend until smooth. Add the milk and Parmesan; blend until smooth. Season with salt and pepper. Add the dill, blend a few seconds, and then blend in the lemon zest.
Transfer the custard to a large bowl. Add the bagel pieces and mix to coat, pressing on the pieces to totally submerge them in the custard. Transfer the mixture to a buttered 9-by-13-inch baking dish. Cover and refrigerate for at least 2 hours and up to 12 hours, pressing on the bagels a few times.
Preheat the oven to 350 degrees F.
While the oven heats, remove the strata from the refrigerator and place on a baking sheet. Bake until puffed and lightly golden brown at the edges and just set in the center, about 40 minutes. Let sit for 15 minutes.
For the caper relish: Combine the capers, dill, tomatoes and onions in a bowl. Season with a touch of salt and pepper. Let sit at room temperature for 15 minutes.
To serve, cut the strata into large round circles (like a bagel) and place on a plate. Top with a few slices of smoked salmon and some of the relish.