Whisk the soy sauce, dry sherry, and cornstarch in a medium bowl until smooth, then add the chicken and turn it to coat; leave it at room temperature for 15 minutes, stirring now and then. The coating should look even and lightly glossy, with no cornstarch settled in dry patches.
Combine every sauce ingredient in a second medium bowl and whisk thoroughly, scraping the bottom to loosen any cornstarch. The mixture should look smooth and uniform before it is added to the skillet.
Heat a large nonstick skillet over high heat until very hot, then add 1 tablespoon of the oil and swirl it around the pan; add the bell pepper, celery, and salt, and stir often for about 5 minutes before moving the vegetables to a large bowl. The vegetables should soften slightly, show a few browned spots, and still retain some crispness.
Return the skillet to high heat, add ½ tablespoon of oil, and cook half of the chicken for about 1½ minutes without moving it too much; turn the pieces and cook for about 1½ minutes more, then transfer them to the bowl with the vegetables. The chicken should turn opaque with lightly golden edges and be cooked through at the center.
Add another ½ tablespoon of oil and cook the remaining chicken for about 1½ minutes on the first side and 1 minute after turning; add the final ½ tablespoon of oil with the garlic and scallions, then stir for about 30 seconds. The garlic and scallions should sizzle sharply and smell fragrant without taking on dark color.
Return the chicken and vegetables to the skillet, pour in the sauce, and reduce the heat to low; stir for about 30 seconds until everything is heated through, then fold in the nuts and adjust the seasoning if needed. The sauce should become clear, thick, and shiny, coating the ingredients without pooling heavily at the bottom of the pan.