Select the Sauté setting on the Instant Pot and heat the vegetable oil. Add the ground beef and sauté until the meat is cooked through and no traces of pink remain, about 8 minutes, breaking up the meat with a spoon as it cooks. Add the onion, carrots, bell pepper, and garlic and sauté for about 5 minutes more, until the vegetables are softened. Stir in the tomato sauce, Sriracha, soy sauce, vinegar, and brown sugar.
Secure the lid and set the Pressure Release to Sealing. Press the Cancel button to reset the cooking program, then select the Pressure Cook or Manual setting and set the cooking time for 20 minutes at high pressure. (The pot will take about 10 minutes to come up to pressure before the cooking program begins.)
When the cooking program ends, you can either perform a quick pressure release by moving the Pressure Release to Venting, or let the pressure release naturally and leave the pot on the Keep Warm setting for up to 10 hours.
Stir the Sloppy Joe mixture, then ladle onto the hamburger buns and top with sliced red onion and pickles. Serve hot.