Adjust rack to top position and preheat oven to 400°F.
While the oven heats, in a large bowl, combine the tomatoes and ½ teaspoon Kosher salt. Let sit for 20 minutes, then gently squeeze tomatoes to release a bit of the juices.
While the tomatoes marinate, make the vinaigrette. In a medium bowl, whisk together the lemon juice, wine vinegar, garlic powder, Dijon, and honey. While whisking, slowly drizzle in the olive oil until emulsified. Season with Kosher salt and freshly ground black pepper, to taste. Set aside until ready to use.
Toss the bagel pieces on a sheet pan with 1 tablespoon olive oil and bake for 7-10 minutes, until toasted and lightly golden, but not too browned.
Once the bagel pieces are toasted, add them to the bowl with the tomatoes. Add the cucumber, red onion, capers, minced dill, minced chives, vinaigrette, and toss to coat. Taste and season with Kosher salt and freshly ground black pepper, as needed.