To start the slaw, place the cabbage and carrot in a salad spinner or colander and sprinkle with the salt. Toss gently and set aside to drain for 15 minutes while you start the chicken.
Sprinkle the chicken thighs with the salt and set aside.
Add the tomato sauce to the inner pot. Add the onion, garlic, chile powder, mustard, vinegar, brown sugar, Worcestershire sauce, and chipotle. Stir to combine. Place the chicken in the pot.
Lock the lid into place. Select Pressure Cook or Manual, and adjust the pressure to High and the time to 8 minutes.
While the chicken cooks, return to the slaw. In a medium bowl, whisk together the vinegar, mayonnaise, horseradish, brown sugar, mustard seed, whole celery seed, and pepper. When the cabbage and carrots have drained for 15 minutes, rinse it and spin or pat dry. Add them to the dressing and toss to coat.
After cooking, let the pressure release naturally for 5 minutes, then quick release any remaining pressure.
Unlock the lid. Use tongs to remove the chicken thighs from the pot to a cutting board. Let cool for a few minutes, then chop or shred with two forks, discarding any fat or gristle.
Using an immersion blender, purée the sauce in the pot. Taste and adjust the seasoning. Return the chicken to the pot and stir to combine.
To serve, spoon the chicken onto the bottom halves of the buns. Finish with a scoop of slaw and the top bun (or serve the slaw on the side).