Turn your instant pot to saute and once hot, add 1/2 tbsp of avocado or olive oil. Dice the onion and red pepper and add to the hot pot. Cook until the onion in translucent, then scrape out into bowl and set aside.
While the onions are cooking mix up the rub. Press the garlic and add to a small bowl with the chili powder, paprika, cumin, oregano and salt. Massage the rub into the chicken breasts.
Once the onion and pepper have been removed add another 1/2 tbsp oil to the instant pot. Once the oil is hot, sear both sides of the seasoned chicken breasts for a minute or so on each side. While the chicken is searing chop up the jalapeños. If you don't like a spicy soup, be sure to remove all the seeds or it'll be super spicy. Remove the chicken once browned and turn the instant pot off.
Deglaze the instant pot by pouring 1/2 cup of the bone stock or chicken broth in and scraping away all the little bits from the bottom of the pot with a wooden spoon.
Add the chicken back into the broth and, without mixing, dump the remaining ingredients on top of the chicken in this order: onion and red pepper, chopped jalapeños, diced tomatoes, tomato paste and lastly the remaining bone stock or chicken broth. Again, do not mix.
Secure the lid of the instant pot and turn the valve from venting to the sealed position. Cook on the Pressure Cook or Manual setting (depending on your model) for 25 minutes, naturally release for 5 minutes, then VERY carefully, using the necessary precautions, quick release.
Once all the steam has been removed, open the lid of the instant pot. Remove the chicken and mix the shredded tex mex cheese into the soup. Use two forks to shred the chicken into chunks and place back into the soup. Mix and serve immediately with your choice toppings!