Combine crushed tomatoes, diced tomatoes, chili powder, cumin, coriander, garlic, onion, carrot, poblano, wheat berries, and 3/4 cup water in a 5- to 6-quart slow cooker. Season with salt and pepper. Cook, covered, until wheat berries are cooked but still chewy, 7 to 8 hours on low or 5 to 6 hours on high. Stir in both beans and cook until warmed through, 8 to 10 minutes. Serve with sour cream, Cheddar, scallions, cilantro, and lime wedges alongside.