There are a multitude of reasons that result in under-eye darkening, including hyperpigmentation of the skin, thin skin with visible underlying eye muscles, allergic conditions, and so on.
In your case the issue looks to be largely pigmentary and can be helped nicely with pigment lasers. We use the picoplus picosecond laser at our clinic with good results for darker skin under-eye pigment management.
The same laser can be used for evening out the over skin tone and texture of the face.
Typically between 3 to 5 sessions are advised with 2 to 4 week intervals, and maintenance and co-management with topical products such as retins and vitamin c serums.
I believe you might have a slight tear trough deformity there too, resulting in a depression and accentuation of the undereye darkening - the photos at this angle dont allow an accurate assessment.
In any case a single session of fillers under the eye can help smoothen that out and brighten the under-eye appearance too.
Cheers and best regards,
Dr Shane Tan