Place mushrooms in a large bowl of salted water. Soak until clean and soft, 8 hours to overnight.
Drain mushrooms, rinse well, and set out to dry on a clean towel.
Preheat oven to 350 degrees F (175 degrees C). Spray a 9x13-inch baking pan with cooking spray.
Chop mushroom stems finely. Cut mushroom caps in half lengthwise; place cut-side up in a 9x13-inch baking pan.
Melt butter in a small skillet over medium heat. Add chopped mushroom stems, red bell pepper, and green onion; cook and stir until green onion is translucent, about 5 minutes. Remove from heat; allow to cool, about 10 minutes.
Mix cream cheese, crabmeat, egg, celery leaves, Worcestershire sauce, hot sauce, and sea salt together in a large bowl. Fold in cooled onion mixture. Place a dollop of filling in each mushroom cap with a small spoon.
Mix bread crumbs and Parmesan cheese together in a small bowl. Sprinkle on top of filled mushroom caps.
Bake in the preheated oven until filling is golden brown, 30 to 35 minutes.