Finely chop grape tomatoes. Mince garlic. Coarsely chop capers. Rinse olives and halve. Stem and coarsely chop oregano. Halve baguette lengthwise.
Make the Sauce
In a small mixing bowl, combine chopped tomatoes, capers, olives, half the garlic (reserve remaining for garlic bread), and half the oregano (reserve remaining for garnish). Add 2 Tbsp. olive oil and season with ¼ tsp. salt and ¼ tsp. pepper. Stir until well combined and set aside for flavors to marry.
Make the Garlic Bread
Combine 1 Tbsp. olive oil and remaining garlic in a small bowl. Spread on cut sides of baguette, place on prepared baking sheet, and transfer to oven. Bake 5 minutes, remove from oven, and add pine nuts to baking sheet. Bake until bread and pine nuts are toasted, 5-6 minutes. While bread bakes, cook pasta.
Cook the Pasta
Add pasta to boiling water and cook, stirring often, until al dente, 3-5 minutes. Reserve ½ cup pasta cooking water before draining. Stir tomato paste into reserved water. Drain pasta in colander and return to pot.
Finish the Pasta
Add tomato mixture and reserved pasta water to pot with cooked pasta. Toss until well combined. Season to taste with salt and pepper.
Plate the Dish
Serve pasta on a plate next to garlic bread. Garnish with pine nuts and remaining oregano.