Finely grate enough ginger on a rasp grater to measure 1 Tbs. (about 1-1/2 inches); set aside. Coarsely chop the remaining ginger and purée in a blender with the celery, fennel, and cup water, about 2 minutes. Strain through a large fine sieve over a medium bowl, pressing hard on the solids with the back of a spoon to extract as much liquid as possible; discard the solids. Stir 3/4 tsp. salt into the vegetable juice until dissolved. Divide the juice among the 4 bags. Put 1 fish fillet and 1 sprig of parsley in each bag. Seal the bags, pressing out as much air as possible, and massage the fish to coat it all over. Refrigerate for 2 to 4 hours to season the fish.
Meanwhile, in a medium bowl, whisk the reserved finely grated ginger, the shallot, 3 Tbs. of the grapeseed oil, the soy sauce, vinegar, olive oil, and red pepper flakes until just combined (the dressing will not be emulsified). Season to taste with salt.
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), 12 to 15 minutes. Transfer the bags to a rimmed baking sheet and let sit for 5 minutes. Meanwhile, heat the remaining 2 Tbs. olive oil in a 12-inch skillet over medium-low heat. Add the garlic and cook, stirring often, until golden, about 1 minute. Add the bok choy and a pinch of salt, cover, raise the heat to medium, and cook undisturbed for 5 minutes, or until the bok choy is crisp-tender. Uncover, stir in the scallions, and remove from the heat.
Divide the bok choy mixture among 4 dinner plates. Using scissors, snip off one corner of each bag and drain and discard the liquid. Open each bag and cut down the center perpendicular to the seal to expose the fish. Using a spatula, lift the fish from the bags and place on top of the bok choy. Spoon the dressing over the fish and the bok choy and serve.