Heat the olive oil in a large pot over medium heat. Add the onion and garlic, sautéing until the onion is translucent, about 5 minutes.
Stir in the diced tomatoes and tomato paste. Cook for another 3 minutes, allowing the flavors to meld.
Pour in the white wine and increase the heat, bringing the mixture to a boil. Simmer for 5 minutes to reduce the liquid slightly.
Add the fish stock, bay leaf, salt, black pepper, paprika, and saffron threads. Bring the stew to a simmer.
Gently place the fish chunks into the pot, followed by the squid. Cook for 10 minutes.
Add the mussels and shrimp to the pot. Cover and cook for an additional 10 minutes, or until the seafood is cooked through and the mussels have opened. Discard any mussels that do not open.
Taste and adjust the seasoning if necessary.
Serve the stew hot, garnished with chopped parsley and accompanied by lemon wedges.