Using highest saute or browning function, heat 1 tablespoon oil in multicooker until shimmering. Add tomatoes, onion, and half of jalapeños and cook until softened, about 5 to 7 minutes. Stir in garlic, 2 teaspoons chipotle, and tomato paste and cook until fragrant, about 1 minute. Stir in broth and tortilla pieces, scraping up any browned bits. Season chicken with salt and pepper and nestle into multicooker.

Lock lid in place and open pressure release valve. Select low slow cook function and cook until chicken is tender, 2 to 3 hours. (If using Instant Pot, select high slow cook function.) Turn off multicooker and carefully remove lid, allowing steam to escape away from you.

Meanwhile, adjust oven rack to middle position and heat oven to 425 F. Toss tortilla strips with remaining 1 tablespoon oil and bake on rimmed baking sheet until crisp and deep golden, 8 to 12 minutes, stirring occasionally. Transfer strips to paper towel-lined plate and lightly season with salt to taste; set aside for serving.

Transfer chicken to cutting board, let cool slightly, then shred into bite-size pieces using 2 forks. Whisk soup vigorously for 30 seconds to break down tortilla pieces. Stir in chicken, remaining jalapenos, and remaining 1 teaspoon chipotle and let sit until heated through, about 2 minutes. Season with salt and pepper to taste. Serve, passing toasted tortilla strips, Cotija, avocado, sour cream, cilantro, and lime wedges separately.