Do I need to do separate dark circle care after under-eye fat repositioning?

It has been about two months since I had under-eye fat repositioning.

Before the surgery, the dark circles looked worse because of the shadows cast by the sunken and bulging areas under my eyes, but now that the contours have been smoothed out, it looks neater than before.

However, some pigmentation remains and is still slightly visible, so it seems there are parts that can be resolved with under-eye tape and others that require separate care. I am curious how people usually manage dark circles that persist even after surgery.