Trim excess fat and skin from the chicken breasts. Sprinkle them on both sides with thyme, salt, and pepper; then dust with flour.
Heat the Instant Pot to Sauté-High. When hot, add the olive oil. Sprinkle with salt. Sear the chicken breasts in the hot oil, turning to brown. Let them cook for about 4 minutes (2 minutes per side). Set them aside in a warm dish.
Add the garlic and sauté for a few seconds until it begins to brown then add the onion and some ground pepper, thyme, and parsley flakes. Sauté until the mixture begins to brown.
Add the carrots and celery. Stir to cook lightly for about 2 minutes.
Add the Marsala and reduce by half. Return the chicken breasts to the pot. Add the remaining seasonings and the quart of broth. Stir to blend the flavors. Cover and reset the Instant Pot to Pressure Cook on high, timed for 15 minutes.
While the stew is cooking, put the cubed potatoes into a microwavable dish along with some water. Cook for about 5 minutes. Potatoes should be tender but not over-soft.
When the Pressure Cooker time is done, slowly release the pressure. Remove the chicken breasts. If you used bone & skin breasts, remove the meat. Chop the chicken breast meat into small pieces (or shred it).
Add the potatoes and chopped chicken meat into the stew, stirring to mix the ingredients. Adjust the salt and pepper to taste.
Cover the pot again, return to LOW pressure for 3 minutes. When done, reduce pressure slowly. Serve in deep plates or bowls.