https://curtjaimungal.substack.com/p/what-is-energy-actually
Ignoring that, saying "energy must exist because of Noether and time-translation" doesn't really tell what energy actually is, not a very satisfactory response
The nature of energy is really just a result of this property.
The difficulties with energy in GR are related to the fact that those equations alone allow for space-times that are truly bizarre. Some that are technically solutions to the field equations are clearly nonphysical (e.g. Goedel's solutions). There is also a priori no reason why e.g. expanding metrics should actually yield proper conservation of energy.
Interesting.
> This is an example of a topic that unstructured self study would likely skip.
I'm not studying physics – could you take a look at some unstructured reflexions I wrote a couple weeks ago?