Turn Instant Pot on SAUTE mode. When hot, add the oil. Add the onion, celery, jalapeño, and garlic. Saute for 5 minutes, then add the chicken, chicken broth, chili powder, salt, paprika, coriander, cumin, pepper, tomatoes, 2 tablespoons cilantro, and lime juice.
Place lid on and lock. Turn on MANUAL mode with high pressure selected for 20 minutes. Turn switch to VENTING and allow for the pressure to release manually, this usually takes 7-10 minutes or so. Remove the lid and stir in remaining cilantro.
Remove chicken and pull into chunks, return to the broth. Place a generous amount of cheese in the bottom of each bowl. Ladle soup over top, then add tortilla strips.