Combine 8 cups water, celeriac, onion and garlic in a large pot. Bring to a boil over high heat, stirring occasionally. Reduce heat to medium, partially cover and cook until the celeriac is tender, 30 to 40 minutes.
Meanwhile, combine sun-dried tomatoes and the remaining 1/2 cup water in a small saucepan. Cook over medium heat until the tomatoes are fully rehydrated and the liquid is almost completely evaporated, 2 to 3 minutes. Drain any excess water. Transfer the tomatoes to a cutting board and let cool for 5 minutes. Mince them and mix with celery, celery leaves, horseradish, oil and capers in a small bowl.
Puree the soup, in batches, until very smooth. (Use caution when blending hot liquids.) Return the soup to the pot to warm over low heat, adding water, if desired, to adjust the consistency. Season with salt. Serve the soup with the tapenade.