1. In a medium bowl, combine the shrimp, ½ teaspoon salt, and the baking soda. Mix well until evenly coated. Set aside at room temperature for 10 minutes or refrigerate for up to 1 hour.
2. Cut the zucchini into noodles using a vegetable spiralizer, according to the manufacturer’s directions. Place the spiralized zucchini in a bowl lined with paper towel or a tea towel to remove any excess water.
3. In a large skillet over medium-high heat, heat 2 tablespoons of the olive oil until shimmering. Add half the shrimp in one layer, cut-side down with the tails sticking up, and cook undisturbed until pink, 1½ to 2 minutes. Flip and cook, turning and stirring the shrimp occasionally, for an additional 2 minutes. Transfer the shrimp to a medium bowl. Repeat with the remaining shrimp, adding more oil to the pan if needed. Set aside.
4. Wipe the skillet clean, return it to medium heat, and add 1 tablespoon of the olive oil, the garlic, and chile pepper. Cook, stirring, until the garlic starts to turn golden brown, about 1 minute. Add the capers and cook for an additional minute, making sure the garlic doesn’t burn.
5. Add the vermouth, raise the heat to high, and stir until the liquid has reduced by half, about 3 minutes. Add the butter and stir until melted. Remove from the heat and stir in the lemon zest, lemon juice, parsley, tarragon, ½ teaspoon salt, and ⅛ teaspoon black pepper. Pour the sauce over the shrimp and toss until well coated; set aside.
6. Wipe the skillet clean, return it to medium-high heat, and add the remaining 2 tablespoons of olive oil. When the oil is very hot, add the zucchini noodles and cook, stirring continuously, for 2 minutes. Transfer the shrimp and all of the sauce to the skillet, mix into the zucchini, and cook for an additional minute. Season with salt and black pepper. Transfer to a serving bowl and serve hot.