Place your black-eyed peas in a fine mesh strainer, rinse well, and set aside to drain.
Press the saute button on your Instant Pot (IP) and heat up the inner pot for 2 minutes (without the lid). Add the carrot, celery, onion, and bell pepper and saute for 5 minutes, stirring occasionally and adding a splash of water if the veggies begin to stick.
Add the garlic, smoked paprika, salt, garlic powder, onion powder, thyme, oregano, and chili powder and stir for 1 minute. Turn off the IP, then add the water and stir up any stuck bits from the bottom of the pot. Stir in the black-eyed peas, potato, and bay leaf, then lock the lid into place, making sure the nozzle is pointed in the sealing position.
Use the Manual (or Pressure Cooking) mode and set the timer for 18 minutes. Use the natural release method when the timer goes off. After 15 minutes, use the quick release method to release any remaining steam from the pot.
While the stew is cooking, stir together the 2 tablespoons of water and arrowroot in a small bowl until smooth and set aside.
When all of the pressure has been released, carefully remove the lid and discard the bay leaf. Add the arrowroot / water mixture, kale, tomato, Worcestershire sauce, lemon juice, and pepper, and stir to combine.