Combine red wine vinegar, balsamic vinegar, garlic, capers, oregano, agave nectar, Dijon mustard, Parmesan cheese, salt, and pepper in an electric blender to make the dressing. Blend, gradually pouring in olive oil, until well combined. Set aside.

Toss chicken breasts with 1 1/2 tablespoons olive oil, Italian seasoning, garlic powder, salt, and pepper in bowl.

Toss tomatoes, bell peppers, and red onion slices with 1 1/2 tablespoons olive oil. Season with salt and pepper.

Slice baguette lengthwise into quarters to get 4 long 'sticks.' Place sticks on a sheet pan and coat with remaining tablespoon olive oil.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Place chicken and sausage on the preheated grill and cook, flipping occasionally until meats are no longer pink in the centers, 12 to 15 minutes. Add vegetable mixture and bread sticks to the grill and cook until moderately charred throughout, about 5 minutes. Transfer cooked items onto a sheet pan for easy transport. Let cool 10 to 15 minutes.

Remove stems and seeds from the grilled bell peppers. Dice peppers, onion, tomatoes, baguette, sausage, chicken, and mozzarella cheese into roughly 1/2-inch pieces. Toss in a large bowl with dressing. Serve over arugula and top with shredded Parmesan cheese.