Is there a case of fat grafting under the eyes while doing eyelid surgery?

I'm worried about my under-eye area...
 My under-eye area is lighter compared to my cheekbones, so I heard that it would be a good idea to do fat
 grafting along with the under-eye area, so I'm worried.
I saw somewhere that I heard that with fat grafting, I'll gradually return to my original appearance.
 Is there a case where the under-eye bags and fat grafting are done together???
Will the fat under the eyes disappear quickly??

They say that the surgical methods for fat grafting and under-eye bags are different, so they can be done separately later, but I want to do anesthesia at the same time...
 But I'm thinking about not doing it if the under-eye fat disappears quickly... I'm worried a lot ㅠㅠㅠ