Place mushrooms in warm water to soak and soften, 10 or 15 minutes. Drain and chop.

Heat butter in a heavy pot or Dutch oven; add sauerkraut and sliced cabbage. Cook over medium-low, stirring occasionally. Brown the meat and add it to pot while sauerkraut is cooking per directions below.

Heat skillet over medium-high heat; add bacon and cook until browned but not crisp. Transfer bacon to pot with cabbage, leaving bacon grease in skillet.

Brown pork shoulder pieces in bacon grease over medium-high heat. Sprinkle with salt. Cook and stir until browned on all sides, 4 to 5 minutes. Transfer pork to pot. Add beef chunks to skillet; sprinkle with salt. Cook and stir until browned, about 4 or 5 minutes. Add sausage slices to skillet and cook and stir until browned. Transfer slices to pot.

Reduce heat under skillet to medium. Add chopped onion and a sprinkle of salt; cook and stir until onion turns translucent and starts to take on some color. Stir in chopped mushrooms and diced prunes. Cook and stir about 2 minutes. Pour in dry red wine; raise heat to medium-high. Simmer until wine is reduced to where very little liquid remains. Transfer onion mixture to pot with cabbage and meat. Add paprika, caraway seeds, thyme, allspice, bay leaf, pepper, and salt. Stir to evenly distribute all ingredients.

Cover tightly; simmer over medium-low heat until meat is tender, 1 to 1 1/2 hours, stirring occasionally. Remove from heat. Allow stew to cool slightly; refrigerate overnight to let flavors blend.

Place pot over low to medium-low heat and add a splash of water. Bring stew to low simmer, stirring occasionally, and cook until hot, 10 to 15 minutes.