Heat olive oil in a large pot over medium heat; cook and stir onion and celery with a pinch of salt until onion is translucent, 5 to 8 minutes. Stir in garlic and cook until fragrant, about 1 minute.
Pour chicken broth and tomatoes into onion mixture. Bring to a simmer and season with paprika, black pepper, and cayenne pepper. Turn heat to low and stir rice into soup; skim foam occasionally and simmer until rice and vegetables are very tender, 35 to 45 minutes. Add sugar.
Blend soup with an immersion blender in the pot until smooth. Whisk 1/2 cup cream into soup and season with salt, black pepper, cayenne pepper, and sugar if needed. If soup is too thick, add more broth; if soup is too thin, cook, stirring often, until reduced and slightly thickened, about 10 minutes
