Pat the chicken dry with paper towels. Tuck the wing tips under, so they sit flat against the chicken, tie the drumsticks together with kitchen twine, then season the chicken all over with the salt, pepper, and paprika. Place the chicken breast side up on the wire metal trivet that comes with your Instant Pot.
Select the high Sauté setting on the Instant pot and heat the olive oil for 2 minutes. Add the onion and garlic cloves and sauté for about 5 minutes, until the onions are softened and translucent. Add the thyme, lemon juice, and chicken broth, and use a wooden spoon to nudge any browned bits from the bottom of the pot. Stir in the halved figs, then add in the potatoes and carrots in an even layer.
Cancel the cooking program to turn off the Instant Pot. Carefully lower the chicken on its trivet into the Instant Pot, sothat it rests on top of the cooking liquid and vegetables. Secure the lid in the Sealing position, then select the Pressure Cook or Manual setting and set the cooking time for 20 minutes at high pressure. (The pot will take about 15 minutes to come up to pressure before the cooking program begins.)
When the cooking program ends, perform a quick release by moving the Pressure Release to Venting.
At this point, if you have an air fryer lid for your Instant Pot, you may use it to brown the top of the chicken. Replace the pressure cooking lid with the air fryer lid, cancel the cooking program, then select the “Broil” setting for 10 minutes. If you do not have an air fryer lid, you may either finish the chicken under an oven broiler for a few minutes, or serve it as is, without browning the skin.
Open the pot and, wearing heat-resistant mitts, grab the arms of the trivet and lift the trivet with the chicken out of the pot. Transfer the chicken to a serving dish. Using a slotted spoon, transfer the vegetables and figs to the serving dish, arranging them around the chicken. Ladle some of the cooking liquid over the vegetables and serve right away.