Heat oil in a medium saucepan over medium-high; add sausage and cook, stirring, until crisp, about 3 minutes. Transfer to a plate.
Add scallions, celery, and thyme to pan; cook until tender, about 4 minutes.
Stir in tomatoes; bring to a boil and cook 3 minutes.
Drain and rinse one can of beans, leaving the second in its liquid; add both to pan with 1 cup water.
Return to a boil, then reduce heat to low and simmer 15 minutes.
If desired, remove 1 cup of mixture and purée in a blender or food processor until smooth, about 15 seconds, then return to pan.
Season with salt and pepper.
Top each serving with cooked sausage, a dollop of sour cream, and a small handful of watercress.
Sprinkle with pepper and celery leaves; serve.
