Pat seafood dry. Cut shrimp and scallops into bite-size pieces; keep crab in chunky flakes.
Warm olive oil and melt butter in a large pot over medium heat.
Soften onion, celery, and carrot in the pot, stirring until glossy, 5–6 minutes.
Stir in garlic and tomato paste; cook until the paste darkens slightly, about 1 minute.
Sprinkle in flour and cook, stirring, 1–2 minutes to form a light roux.
Deglaze with white wine, scraping up any browned bits. Simmer until slightly reduced, 2 minutes.
Pour in seafood stock. Add Old Bay, paprika, thyme, cayenne, salt, and pepper. Simmer 10 minutes.
Blend the soup base with an immersion blender until smooth and velvety.
Lower heat. Stir in heavy cream and return to a gentle simmer.
Add shrimp and scallops. Simmer gently until just cooked, 4–5 minutes. Fold in crab for 1 minute.
Finish with lemon juice. Taste and adjust seasoning. Ladle into bowls and garnish with parsley.