Which is better for improving hollowness under the eyes, fillers or fat redistribution?

Lately, when I take photos, the area under my eyes looks particularly sunken and shadowed, like dark circles, so I'm worried. Even on days when I'm not feeling bad, people often tell me I look tired, so I started looking into under-eye procedures. I found that there are under-eye fillers to add volume to sunken areas and under-eye fat repositioning to redistribute bulging fat, but I'm not really sure what the difference is.

If my main concern is hollowness rather than significant under-eye fat protrusion like mine, would fillers be a more suitable option? I am wondering if fat redistribution can also improve the sunken areas. I am a bit worried because I have heard that fillers need to be re-injected over time, and that the results might not look natural since the skin under the eyes is thin.

I would like to know which of the two methods actually yields higher satisfaction, and what I should check before the procedure. Rather than opting for a major procedure, I want to find a method that is tailored to my eye condition, is less burdensome, and offers natural improvement. I would appreciate advice from those with experience!