Combine pork, coriander, half of garlic, and 1 tablespoon salt in a large bowl; season with pepper and toss. Cover; chill at least 4 hours.
Preheat oven to 350°F Toast pumpkin seeds on a rimmed baking sheet, tossing occasionally, until golden, about 5 minutes; set aside.
Toast chiles on clean baking sheet until slightly darkened, about 5 minutes. Let cool slightly, then remove stems, and seeds, if you prefer less heat. Place chiles, half of yellow onion, remaining garlic, and 1 cup hot water in a blender; let sit 10 minutes to soften chiles. Blend until smooth; set chile purée aside.
Heat oil in a large Dutch oven over medium-high heat. Working in batches, cook pork, turning occasionally, until browned, 8–10 minutes; transfer to a plate.
Pour off fat from pot. Cook chile purée in pot over medium-high heat, stirring occasionally, until reduced by half, 8–10 minutes. Add pork, oregano, remaining yellow onion, and 10 cups water to pot; season with salt and pepper. Bring to a boil, reduce heat, and simmer, partially covered, skimming occasionally, until pork is very tender, 3–3 1/2 hours.
Add squash to stew and cook, uncovered, until pork is falling apart and squash is soft, 30–35 minutes; season with salt and pepper.
Toss red onion and lime juice in a small bowl; let sit, tossing occasionally, 30 minutes.
Serve stew with red onion, cilantro, and reserved pumpkin seeds.
DO AHEAD: Pork can be marinated 2 days ahead; keep chilled. Stew can be made 3 days ahead; let cool, then cover and chill.