Drain the sauerkraut and reserve the brine. Taste the sauerkraut and if you find it much too strong, rinse it until you like the way it tastes -- keeping in mind that the flavor will be diminished when it is cooked with the other ingredients. Drain well and set aside.
Heat the broth in the pressure cooker. Set the dried mushrooms in a bowl and pour the hot broth over, submerging them in the broth with the back of a spoon. Cover with a plate and set aside until the mushrooms are soft, about 10 minutes.
Meanwhile, rinse and dry out the cooker. Heat the butter and oil over medium-high heat. Brown the pork and kielbasa in 3 or 4 batches, about 4 minutes per batch, adding more oil if needed. Set aside.
With a slotted spoon, remove the reconstituted mushrooms from the broth and squeeze them over the bowl to catch the liquid they release. Coarsely chop the mushrooms if the pieces are large. Carefully pour the broth into the cooker, taking care to leave behind any sediment on the bottom. Set the cooker over medium heat and stir well to scrape up any browned bits stuck to the bottom. Add the mushrooms and half of the sauerkraut. Set the browned pork and kielbasa on top. Cover with the remaining sauerkraut and sprinkle caraway seeds on top. Set the potatoes and parsnips on the kraut.
Lock the lid in place. Over high heat, bring to high pressure. Reduce the heat just enough to maintain high pressure and cook for 10 minutes. Quick-release the pressure. Remove the lid, tilting it away from you to allow excess steam to escape.
Ladle out 1/2 cup of the broth and blend the sour cream into it. Then stir this mixture back into the pot as you stir well to distribute all of the ingredients. If you'd like a stronger sauerkraut flavor, add some or all of the reserved brine. Season with salt and pepper. Sprinkle lightly with dill. Pass additional sour cream in a bowl at the table.