Do a chore? Take a rest. Do a hobby? Fake a rest. Exercise? Long rest. Break up an argument between my kids? Rest. Everything is rest. I feel like half my life is waiting for my mental energy to come back. Not physical. I can do the task, but convincing the rest of my body to do the thing takes rest.
Serious response, damn, I feel you some days. I mean, I'm dealing with physical limitations via disability, but it's the mental side that is harder.
Ever run into the "spoon analogy"? If not, look it up. While it's geared towards disability, it applies to mental health just as well. And I don't mean mental health in the way people have started using it to mean crazy or messed up. I mean it in the older sense that our minds require the same degree of upkeep our bodies do. More sometimes.
You're running out of spoons. Just not enough left over after mandatory tasks to ever get rest, you're faking rest to yourself just to keep going. I've been there, my lemmy homie.
It might actually be time to talk to your doctor about energy levels, just to be on the safe side though. You'd be surprised how often that kind of state can come from an unnoticed nutritional deficit, or something similar. That kind of thing impacts mental energy just as much as physical. Never hurts to be sure.