In a bowl, combine all the meats, gently mixing to avoid overmixing. Shape and press the mixture into six patties, about 1/4 inch (6 mm) thick. Press a divot into the center of each patty with your thumb. Season the outsides of the patties well with salt and pepper. Place three patties on each cooking tray, divot side down. Lightly spray both sides with cooking spray.
Place the drip pan in the bottom of the cooking chamber. Using the display panel, select Air Fry, adjust the temperature to 375°F / 190°C, and set the time to 9 minutes. Preheat the Instant Pot Vortex® until the display indicates Add Food.
Place the cooking trays in the bottom and middle positions. When the display indicates Turn Food, flip the patties over so they are divot side up and switch the bottom cooking tray to the top position and the middle cooking tray to the bottom position. Cook until the patties are lightly browned, the juices run clear when pierced, and the internal temperature reads 160°F / 71°C on a meat thermometer.
Place a cheese slice on top of each burger. Using the display panel, select Broil, adjust the temperature to 400°F / 200°C, and set the time to 2 minutes. Preheat the Instant Pot Vortex® until the display indicates Add Food. Place the cooking trays, one at a time, in the top position and cook until the cheese is melted.
Mayonnaise Sauce: Meanwhile, in a small bowl, combine mayonnaise, ketchup, and relish; mix well.
To assemble, spread the Mayonnaise Sauce over the inside of the buns, place the burger on the bottom half, and garnish with toppings of your choice.