Some yoga poses are more equal than others. In terms of difficulty there are 2 that get a lot of press headstands and backbends. Given the dangers of headstands to the neck the benefits of this inversion are iffy at best so the skin-friendliest yoga pose remains the backbend - the wheel pose - the inverted U pose.
The most important reason backbends benefit the skin is the reprieve from bending forward - at desks and cars or even checking smartphones we find ourselves leaning forward. This is great - there is incalculable value in momentum and progress. But as a skin and body habit it's hardly optimal because of its repetitive motion. Repair always involves stepping back from a repetitive routine.
In every backbend there is an element of defying gravity and letting the blood rush into your head and face in a way that feels out of the ordinary - it is in embracing this upside down perspective and coaxing a novel flexibility in the spine - it's a little bold step outside the familiar and boldness like everything else is a muscle that benefits from practice.
A full wheel pose opens the heart chakra releasing tension in the chest and is even recommended as a cure for depression. Not only does it open up the chest but stretches the shoulders to improve posture and free up breathing. This correction of the posture is the best thing to happen to the skin of your face - standing tall and looking straight instead of down improves the elasticity of the skin under the neck. Strengthening the spine's flexibility also improves circulation to the brain and cleanses the nervous system.
Working your way to building a backbend practice is a discipline in and of itself. To start with the cobra pose that's part of the sun salutation and then the deceptively simple bridge pose then the camel pose and finally the glorious wheel pose is an achievement your skin and body will benefit from disproportionately. B.K.S Iyengar has this to say and what's true of the spine is doubly true of the skin.
With backbends, you have to be cautiously bold. Not carelessly bold. You have to descend to the dictation of the spine. You cannot command from the brain to do the poses. As you play with a child, guarding the child from injuries, similarly you have to play in backbends, guarding your spine.