Shurink isn't a procedure necessary only for people with a lot of facial fat, right? Also, how painful is it?

I tend to have very little fat on my face.
Whenever I heard the word "lifting," I was scared that my face might sink in even more.

However, I heard that sagging skin and having a lot of fat are separate issues.

I've heard that even if you have little facial fat, some people still consider a lifting procedure due to skin elasticity or sagging.
In cases like this, shouldn't I just judge based on how much fat is on the face?
And how severe will the pain be?