There is fat herniation of the medial fat pads in the lower lids. This is best treated with a transconjunctival approach where the incision is located inside the lower lids. Removal of the bags will also remove the shadow effect created by the puffy bags. The dark pigmentation of the skin itself will not change with any surgery
How to Get Rid on my Dark Circles Under my Eyes (photo)?
Doctor Answers 2
Dark circles and puffy eyes
The photo is helpful, but an in-person evaluation is more valuable. In general, there are three reasons why the skin around the eyes can be [or seem] darker:
1. The thin eyelid skin allows the darker muscle underneath to show
2. The hollowness around the eyes can create a shadow effect that exacerbates darkness. This is further amplified if you have some fat prolapsing in the eyelid making a contour irregularity.
3. Skin pigmentation [sometimes from blood products from bruising] If it is blood product pigmentation, it could last months to improve.
Depending on which of the above is the issue, different modalities may be helpful [time, fillers, laser resurfacing, concealer etc].
Based on the photo, I think your issue is a combination of 1 and 2. Fillers are probably your best option to minimize this, but it will not remove the discoloration, just camouflage it a bit better.