There is a fundamentally covariant formulation of GR based on light cones, in which the spacetime points themselves have canonical poisson brackets. This formulation is coordinate and “background spacetime” independent. When you quantize this, the points themselves become the quantum observables subject to commutation relations. See https://arxiv.org/abs/gr-qc/9603061
We did this for the linearized gravity, quantum spacetime in this picture is continuous, covariant and fuzzy.
I’m sorry to hear Jakob Beckenstein is dead. He was an incredibly original thinker not as widely recognized for his work on BH thermodynamics as he should have been and a wonderful human being.