Heat the oven to 350°F and butter a 9×13-inch baking dish. Coat the corners and bottom evenly so the sauce and pastry release more easily after baking.
Warm the cream of chicken soup, 3/4 cup grated cheddar cheese, and 1/2 cup heavy whipping cream in a small pot over medium heat. Stir until the cheese disappears into a smooth sauce, then remove the pot from the heat.
Mash the room-temperature cream cheese, room-temperature butter, and garlic powder together in a mixing bowl with a fork. The mixture should look soft and uniform with no firm bits of cream cheese remaining.
Stir in the chopped chicken, onion, 1/2 cup finely grated cheddar cheese, seasoning salt, black pepper, and 2–4 tbsp heavy whipping cream. The filling should hold together and feel creamy enough to scoop without becoming runny.
Separate and unroll the crescent dough, then place 1 level tablespoon of filling on the wide end of each triangle and roll toward the pointed end. Keep the filling centered and tuck the dough around it so the seams stay closed as the rolls expand.
Spoon a thin coating of the cheese sauce across the bottom of the buttered dish. The sauce should lightly cover the dish rather than form a deep pool beneath the pastry.
Set the filled crescent rolls over the sauce in the baking dish. Arrange them snugly with a little space for the dough to puff and brown.
Pour the remaining cheese sauce over the rolls. Leave some dough exposed on top so it can develop a golden, flaky finish.
Scatter the grated cheddar cheese over the casserole. The cheese should cover the rolls lightly and melt into the sauce as it bakes.
Bake for 30 minutes. The casserole is ready when the tops are golden, the edges bubble actively, and the kitchen smells buttery and savory.