In a large skillet, add the water, soy sauce or tamari, honey or maple syrup, and white parts of the scallions. Place the fillets into the skillet, skin side up. Turn the heat to high and bring to a boil/rapid simmer. Reduce the heat to low and simmer gently for 8-10 minutes or until cooked through, turning the fillets halfway through. You may need to flip the fillets again if they need to be cooked more in the center. The time will depend on how thick the fillet is. Transfer the fillets and scallions to a plate.
Add half of the chard and sliced stems to the skillet and simmer until wilted down, about 2 minutes, stirring occasionally. Add the remaining chard and stems and cook until wilted, about 2 more minutes. Use tongs to transfer to a bowl (leave the broth behind, we’ll use it later). Chop up the cooked scallions and add them back in with the chard.
In a small bowl, whisk together the olive oil, lime juice or vinegar, sesame oil, and ginger. Add the snap peas and dressing to the bowl and toss to coat.
Serve the chard topped with fish and avocado. Sprinkle with the green parts of the scallions and sesame seeds. Pour the reserved poaching broth over everything.