Line a slow cooker with a slow cooker liner and spray with cooking spray. Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease. Whisk together eggs, milk, dry mustard, garlic powder, onion powder, salt, and pepper in a bowl. Spread 1/3 hash browns, 1/3 cooked sausage, and 1/3 Cheddar cheese into the bottom of the prepared slow cooker. Repeat layers in that order with remaining hash browns, sausage, and Cheddar cheese. Pour egg mixture on top. Cook on Low until eggs are set, 6 to 8 hours.