Season chicken thighs all over with salt. Heat 2 Tbsp. oil in a large Dutch oven or other heavy pot over medium-high. Working in 2 batches, cook chicken, skin side down, until skin is golden brown, 8–10 minutes. Transfer chicken to a plate.

Cook onion in same pot, stirring often, until softened and edges are browned, 8–10 minutes. Add garlic and cook, stirring often, until softened, about 2 minutes. Add paprika and cook, stirring, until fragrant, about 30 seconds.

Add tomatoes and smash with a wooden spoon until no pieces are bigger than 1/2". Bring to a simmer and cook until tomatoes are slightly thickened, 6–8 minutes. Add stock, potatoes, and chicken and return to a simmer.

Reduce heat to medium-low and cook, stirring occasionally and adding more stock if needed to keep potatoes submerged, until chicken is very tender and potatoes are creamy, 75–90 minutes. Remove from heat; taste and add more salt or paprika if needed.

Squeeze juice from lemon into a small bowl and stir in sour cream; season with salt. Toss radishes and a pinch of salt in another small bowl.

Transfer stew to a platter and drizzle sour cream over (you can also serve alongside if you prefer). Top with radishes, drizzle with a little oil, and season with lots of pepper.