Arroz Verde With Spiced Mushrooms

Name: Arroz Verde With Spiced Mushrooms
Ingredients: 3 limes, divided; 2 medium jalapeños, stems removed; 5 garlic cloves; 2 cups (packed) cilantro leaves with tender stems, plus more for serving; 3 tsp. Diamond Crystal or 1½ tsp. Morton kosher salt, divided; ½ cup sour cream; 2 Tbsp. mayonnaise; 1½ cups jasmine or other long-grain rice; 6 Tbsp. vegetable oil, divided; 1½ tsp. ground cumin, divided; 1½ lb. mixed mushrooms (such as oyster, shiitake, maitake, and/or crimini), torn into various sizes; 1 tsp. paprika; Freshly ground pepper