Adjust oven rack to lower-middle position; heat oven to 350 degrees.
Toss shrimp, 1/4 teaspoon salt, 1/4 teaspoon black pepper, 1 tablespoon oil, and 1 teaspoon garlic in medium bowl; cover with plastic wrap and refrigerate until needed.
Season chicken thighs with salt and pepper; set aside.
Heat 2 teaspoons oil in large Dutch oven over medium-high heat until shimmering but not smoking. Add peppers and cook, stirring occasionally, until skin begins to blister and turn spotty black, 3 to 4 minutes. Transfer peppers to small plate and set aside.
Add 1 teaspoon oil to now-empty Dutch oven; heat oil until shimmering but not smoking. Add chicken pieces in single layer; cook, without moving pieces, until browned, about 3 minutes. Turn pieces and brown on second side, about 3 minutes longer; transfer chicken to medium bowl. Reduce heat to medium and add chorizo to pot; cook, stirring frequently, until deeply browned and fat begins to render, 4 to 5 minutes. Transfer chorizo to bowl with chicken and set aside.
Add enough oil to fat in Dutch oven to equal 2 tablespoons; heat over medium heat until shimmering but not smoking. Add onion and cook, stirring frequently, until softened, about 3 minutes; stir in remaining garlic and cook until fragrant, about 1 minute. Stir in tomatoes; cook until mixture begins to darken and thicken slightly, about 3 minutes.
Stir in rice and cook until grains are well coated with tomato mixture, 1 to 2 minutes. Stir in chicken broth, wine, saffron, bay, and 1/2 teaspoon salt. Return chicken and chorizo to pot, increase heat to medium-high and bring to boil, uncovered, stirring occasionally. Cover pot and transfer to oven; cook until rice absorbs almost all liquid, about 15 minutes.
Remove pot from oven (close oven door to retain heat). Uncover pot; scatter shrimp over rice, insert mussels hinged side down into rice (so they stand upright), arrange bell pepper strips in pinwheel pattern, and scatter peas over top.
Cover and return to oven; cook until shrimp are opaque and mussels have opened, 10 to 12 minutes.
Let paella stand, covered, about 5 minutes. Discard any mussels that have not opened and bay leaf, if it can be easily removed. Sprinkle with parsley and serve, passing lemon wedges separately.