Preheat oven to 400 degrees. Process bread in a food processor until coarse crumbs form. Spread onto a rimmed baking sheet. Toast in oven, stirring occasionally, until golden brown, 5 to 7 minutes. Transfer breadcrumbs to a shallow bowl; let cool completely. (Leave oven on.)
Rinse chard, but do not dry. Heat oil in a large skillet over medium heat. Add shallot and half of the garlic; cook, stirring, 1 minute. Stir in chard and 1/4 teaspoon salt. Cover, and cook until chard has wilted, about 10 minutes. in stock. Cook, covered, until chard is very tender, about 12 minutes. Stir in vinegar, and cook, uncovered, 5 minutes. Remove from heat; cover to keep warm.
Coat a 13-by-9-inch baking dish with cooking spray; set aside. Add remaining garlic, the sage, parsley, zest, cayenne, and 1/8 teaspoon each salt and black pepper to breadcrumbs; stir. Put flour and egg white into separate shallow bowls. Season both sides of fish with remaining 1/8 teaspoon each salt and black pepper. Working with 1 fillet at a time, dredge in flour, shaking off excess; dip into egg white then into breadcrumbs, turning to coat. Transfer to prepared dish. Bake until fish flakes easily, 15 to 20 minutes. Divide fillets and chard among 4 plates. Serve with lemon wedges.