Can under-eye fat repositioning be considered even if the under-eye area isn't very bulging?

The first thing that catches my eye is that the area under my eyes looks tired.

It wasn't severely bulging or protruding fat, but depending on the lighting, shadows formed, making me look older than I actually am.

I try covering it with concealer, but it seems to just make it look thicker, so I'm looking for another method 😮

Is under-eye fat repositioning a surgery performed only when there is a significant amount of protruding fat, or can I consult about it even if I am concerned about under-eye shadows or boundaries like me?