Combine the saffron rice, 1 1/4 cups water, and a pinch of salt in a small saucepan. Bring to a boil, cover, and reduce heat to low. Cook until all of the water is absorbed and the rice is tender, about 15 to 20 minutes. Rinse and dry the produce.
Drain and rinse the cannellini beans. Thinly slice the Swiss chard stems and roughly chop the leaves. Peel and mince the garlic. Peel and mince the shallot. Place a large pot over medium-high heat with 2 tbsp olive oil. Once hot, add half of the garlic and half of the shallot, and a pinch of salt, and cook until softened, about 3 to 5 minutes.
Add the chopped Swiss chard stems to the large pot and cook until softened, about 1 minute. Add the paella seasoning, cannellini beans, 3 cups water, and a good pinch of salt and pepper. Bring stew to a simmer while you make the chimichurri.
Finely chop the parsley leaves. Finely chop the cilantro leaves and tender stems. Add the parsley, cilantro, dried oregano, and capers to a medium bowl along with the remaining shallot and garlic. Add the red wine vinegar, 3 tbsp olive oil, and ¼ tsp salt. Stir chimichurri well to combine.
Add the Swiss chard leaves to the simmering stew, and cook until the greens have wilted, about 2 to 3 minutes. Halve the lemon, and add juice from half to the stew. Taste and season with salt and pepper. Cut the remaining lemon half into wedges.
Ladle the Spanish-style white bean stew into large bowls. Top with saffron rice and drizzle with chimichurri. Serve with lemon wedges.