Start the potatoes. Heat the oven to 425°F (220°C), conventional heat. Scrub and dry the potatoes, pierce each several times with a fork, and rub with the oil and ¼ teaspoon salt. Place on a rimmed baking sheet without wrapping in foil.

Bake until soft. Bake for about 45–60 minutes, turning once, until a knife slides into the centers easily and the flesh yields when gently pressed with an oven mitt. Remove smaller finished potatoes first if needed. The filling is easiest to prepare near the end of this baking stage.

Mix the slaw dressing. Whisk the yogurt, vinegar, Dijon, remaining ¼ teaspoon salt, and pepper in a bowl. Fold in the cabbage and half the green onions. Cover and refrigerate until serving so the topping stays cool and crisp.

Heat the chicken filling. Combine the fully cooked chicken, barbecue sauce, and water in a saucepan. Cover over medium-low heat, stirring regularly, until thoroughly hot and reheated to 165°F (74°C). Add small splashes of water if it starts sticking before the center is hot.

Open and fill. Let the baked potatoes sit just long enough to handle safely. Cut a slit lengthwise into each and gently loosen the flesh with a fork. Divide the hot chicken filling among the four potatoes, keeping the cut sides open enough to hold it.

Add the cool topping. Spoon the slaw over the warm filling and finish with the remaining green onions. Serve promptly. If preparing for later, keep potatoes, chicken, and slaw in separate containers and assemble only after reheating the hot components.