Heat a large soup pot over medium-high heat and add the sausage. Cook until the sausage is caramelized and the fat is rendered, 4 to 6 minutes. Add the onions and celery and cook, stirring occasionally, until vegetables are soft and lightly browned, about 4 minutes. Add the garlic and cook, stirring, for 1 minute. Add the cider and cook until almost completely reduced. Add the sauerkraut, broth, potatoes, thyme and pepper and bring to a boil. Reduce the heat to a low simmer and cook, stirring occasionally, until potatoes and sauerkraut are very tender and the broth is flavorful, 45 minutes to 1 hour. Taste and adjust the seasoning, if necessary. Serve immediately, with hot, crusty bread on the side.