Not to bring up an older thread, but this is an interesting topic. Most of the conceptual subtleties around conservation of energy in quantum gravity are already contained in classical GR. If you have a spacetime with an asymptotic null/timelike boundary, then energy can be defined at infinity and has conservation laws associated to it. What this actually defines is a Hamiltonian at infinity which generates time evolution. In canonical quantum gravity this boundary Hamiltonian can be quantized, with all the usual subtleties (but nothing specific to conservation of energy).
In the bulk of the spacetime we just have the Hamiltonian constraint. This basically says there's no gauge-invariant bulk notion of energy/time. It is famously difficult to construct a Hilbert space of states which satisfies the Hamiltonian constraint in higher dimensions, but again nothing really related to the conceptual issues surrounding conservation of energy.
In classical GR, one way to get a meaningful notion of bulk energy is via the covariant phase space formalism applied to finite boundaries in the bulk. For example you can treat the event horizon as a boundary of the exterior and define quasi-local charges on cuts of the horizon associated to bulk diffeomorphisms. This essentially acts as a Hamiltonian for exterior degrees of freedom. This will satisfy conservation laws as usual. But this is much trickier to achieve in quantum gravity, where the bulk spacetime fluctuates (and can even have topological changes), hence making it difficult to precisely defined a finite boundary in the bulk spacetime, though it can be done via constraints. Once again, nothing about quantum gravity adds conceptual depth to the notion of energy in gravity. It's already quite deep in GR.