Hoping to add my experience to the thread. 2021 Silverado LTZ 5.3, 1500 miles. Stuck in Park, unable to ******, no click when brake applied. Turn off vehicle and warnings says "shift into park". Warning light and alarms. Pulled negative cable. Towed to dealership. Diagnosed shift actuator failure. Part 84800776 installed. For reference it looks like 84800776 is for 6 and 8 speed trans. Part 84800777 is for the 10 speed.
HTH