Combine the soda, balsamic vinegar and 1/8 teaspoon of salt in a saucepan over medium-high heat and reduce to 1/2 cup, about 20 minutes. Remove from heat.
Heat 1 teaspoon olive oil in a large non-stick skillet over medium heat. Add mushrooms, 1/2 tablespoon of water and a pinch of salt. Cook just until tender, about 2-3 minutes. Add remaining vegetables and toss to combine. Remove from heat and hold while cooking fish.
Season salmon fillets with remaining salt and pepper. Heat remaining olive oil in a non-stick skillet over medium heat. Place the fillets, flesh-side down into the pan. Sauté until first side is golden brown, about 5-7 minutes. Flip over to skin side. Sauté until fish is opaque, but still tender, about 5 additional minutes. Remove from heat and hold warm.
Place the pan with vegetables over medium-high heat and toss to reheat briefly. Serve fillets and mixed vegetables, drizzled with glaze.