Pat the fish dry and season on both sides with 1 tsp. salt total. Transfer to a plate, cover with plastic wrap, and chill for 1 to 2 hours.
Have ready a small, fine strainer set over a small heatproof bowl. In a 1- to 2-quart saucepan, melt the 3/4 cup butter with 4 of the lemon slices over medium heat, swirling frequently, until the milk solids turn golden-brown, 6 to 8 minutes. Immediately strain the butter, pressing on and then discarding the lemon slices. Let cool to room temperature.
Divide the butter and the remaining 4 lemon slices among the 4 bags. Put 1 piece of fish in each bag. Seal the bags, pressing out as much air as possible, and gently massage the fish to coat it all over.
Fill a 4-quart pot with 3 inches of water and clip a deep-fat, probe, or instant-read thermometer to the side of the pot. Heat the water slowly over low heat to 140°F, about 15 minutes. Put the bags of fish in the water (the tops of the bags can stick out) and cook, maintaining a water temperature of 135°F to 145°F, until the center of the fish registers 130°F to 135°F on an instant-read thermometer (open the bags to check), 10 to 12 minutes. Transfer the bags to a rimmed baking sheet and let sit for 5 minutes.
Meanwhile, melt the remaining 2 Tbs. butter in a 12-inch skillet over medium heat until foamy, then add the mushrooms and a pinch of salt. Cook, stirring often, until the mushrooms are light golden, 3 to 5 minutes. Add the peas and 2 Tbs. of water and cook, stirring often, until the peas are bright green and crisp-tender, about 2 minutes. Add 1/4 tsp. of the sesame seeds and the red pepper flakes, then season to taste with salt.
Using scissors, snip off one corner of each bag and drain the butter into a small bowl. Stir the lemon juice into the butter and set aside. Divide the mushrooms and sugar snap peas among 4 dinner plates. Open each bag and cut down the center perpendicular to the seal. Using a spatula, lift the fillets from the bags and arrange on top of the vegetables. Pour the reserved lemon-butter mixture over the fish, garnish with the lemon slices and the remaining 1/4 tsp. sesame seeds, and serve.