Set the Instant Pot to the sauté setting, and add the butter. Add the vegetables and a pinch of salt; sauté until softened, about 5 minutes.
Add the stock, wine (if using), chicken, thyme, bay leaf, and a teaspoon of salt. Cook at high pressure for 6 minutes; release pressure manually. Use tongs to remove the chicken and set aside to cool.
While the chicken is cooking, make the dumplings. Whisk together flour, baking powder, and salt, then add the butter and milk. Stir to combine; you may have to finish combining with your fingers.
If you are making drop dumplings, set aside. Otherwise roll the dumpling dough on a floured surface into a ½-inch thick square, about 12 by 12 inches. Cut into 1-inch by 2-inch rectangles.
Once the chicken is cool enough to handle, shred into bite-size pieces.
Add the chicken to the broth and turn on the sauté setting. If you’re making drop dumplings, pinch off bite-size pieces of the dough. When the broth comes to a simmer, start adding the dumplings a few at a time. Add more each time the broth comes back to a simmer, using a slotted spoon to gently push the dumplings down into the liquid. Do not stir.
Once all of the dumplings have been added to the pot, cook for 8–10 minutes, or until dumplings have puffed and cooked through. Adjust salt and pepper to taste and serve.
If you are using any of the optional finishes, add them when the dumplings are finished and bring back to a simmer. Turn off Instant Pot and serve. (This stew will be thicker on day two.)