Kartik Prabhu
The canonical energy as given in Hollands-Wald is gauge-invariant up to “boundary terms”. To avoid this awkwardness, Hollands-Wald partially fix the gauge at the horizon (and infinity appropriately) by requiring vanishing perturbed area and perturbed expansion.
One can choose to not gauge-fix but instead modify the canonical energy definition itself by adding certain boundary terms so that the modified one is completely gauge-invariant.