the spoons thing is just a useful metaphor to explain some of the ways metal illness affects one's day-to-day life. i use it when talking to people who have a hard time understanding what depression/anxiety means for me personally.
neeko being exhausted for days after doing something so intense is something that i experience too.
While the term has primarily been used in the mental illness context, I think it applies more broadly, too. Because consciousness is a biological process, it makes sense that the same rules of exhaustion apply to the brain as to muscles: both can get exhausted after using them for long enough. It's just that for people with mental illness, this limit is much more apparent, just like a person with an arm injury will not be able to carry heavy stuff very far. Then again, a bodily injury is often obvious to an outside observer, while mental illness is not, and furthermore, things like maintaining focus for prolonged periods of time is taken for granted by those who've never suffered from mental illness.
TL;DR: Everyone has a limited number of spoons to give, but only people living with mental illness have to ration them in day-to-day life.