Make the sofrito. Heat a 12-inch paella pan over medium-high heat. Add 3 Tbsps. oil, then the onions and cook, stirring frequently, until the onions are softened, 3 to 5 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Stir in the grated tomatoes and cook, stirring frequently, until the tomatoes have lost most of their moisture and the sofrito is reduced to about one-fourth cup, 8 to 10 minutes. Remove from heat and place the sofrito in a small bowl. Wipe the pan.
Return the pan to medium-high heat. When the pan is hot, add the remaining oil, then the cod and squid. Sear the fish, stirring frequently, about 1 minute. Reduce the heat to medium and add the sofrito back to the pan. Cook, stirring the sofrito with the fish to blend the flavors, for 3 minutes. Add the wine, stirring to remove any bits of flavoring from the bottom of the pan. Cook until the wine is reduced by half, about 1 minute.
Stir in the fish broth, then add the saffron and bay leaf. Season with the salt; the broth will be a bit salty at first, but will even out as the rice cooks.
Spread the rice evenly in the pan. The rice should be completely submerged; if not, add more broth to the pan. Do not stir the rice. Bring the mixture to a boil over high heat, then reduce the heat to a gentle simmer. Arrange the mussels and shrimp over the rice and continue to cook, being careful not to break the film that forms on the surface of the rice or the rice will not cook evenly. Rotate the pan as needed so the paella cooks evenly. Cook until the liquid is mostly absorbed by the rice, the shrimp are firm and opaque and the mussels have opened, about 10 minutes. Remove from heat.
Cover the pan loosely with paper towels and rest for at least 5 minutes before serving at warm room temperature. The paella can remain at room temperature for up to 2 hours, covered, before serving.