I really like the "energy vs. information" framing. And I think everything you've said about energy and its properties is right on the money. But I do believe that it is probably information all the way down. Why?

Because each "energy" you've mentioned can be measured by the information that describes it. Yes, a wave is driven by energy while we only perceive its information. But the information is still relevant. So, why would it be that God/higher powers are not entities that can be likewise measured by their information? Perhaps God radiates energy into the universe like waves - undulations and fluctuations - but this is likely still measurable. So, whatever "God" is, its complexity is probably more similar to a CPU (i.e. immense processing power that is measurable and determined by its information) than a mystical and indeterminate force.