Is dark circle surgery (under-eye fat repositioning) originally like this.....

I’ve been searching for 3 nights and 4 days,... but there are hardly any people who have had only dark circle surgery... and there really isn’t much information... so I’m just openly asking here. I have pretty blue-colored circles pressing under my eyes, and when I’m on my period, they get even darker, as if I had stuck a sign on my eyes saying, 'I’m on my period~' When I went for a nose consultation, the doctor pointed it out anyway and said this dark circle surgery should come first. He didn’t call it dark circle surgery; he called it under-eye fat repositioning or something like that. For the surgery, - there’s an operation where they make an incision right under the eye, so from the outside (it seems like they cut about 2 cm), and - there’s an operation where they cut inside the eye. The methods are - tidying up the eye fat (they shouldn’t remove fat. I already don’t have much fat), and - tidying up the eye fat and putting in a little fat from the thigh or another area.. My questions are these. 1. If fat from other skin is put into the eye area, won’t it be absorbed? Won’t fat from another area float around loosely? 2. Doesn’t the surgery that cuts the outside of the eye leave scars? Even small scars last a long time on my face, so the idea that a roughly 2 cm incision leaves no scar (I saw post-op photos and there really were no scars, but I can’t tell if they used Photoshop) doesn’t make sense. 3. But if it’s an operation cutting inside the eye, wouldn’t it be a bit difficult for me since I wear contact lenses? 4. After a long time, wouldn’t the fat probably sag again, so I’d have to redo it? 5. The most important thing is a specialized clinic, but since there really aren’t places specializing in dark circles, I asked while getting my nose consultation. They said ㅊㅇ style is around 1.8 million won and ㄱ세ㅇ is 1.5 million won (there, they said they remove a little fat and reposition it...) Is the price originally this expensive.. Anyway, if anyone has had surgery for under-eye sagging and had even a little success, please don’t pass this by.... Please.