There are two different things at play here, which is probably what's causing the confusion:
Choosing a skin = picking which overall control panel system you use — Evolution vs Enhanced. These look and behave completely differently; Enhanced is the older classic layout, Evolution is the newer one you're currently on. This isn't something found inside Evolution's own settings pages — it has to be set at the account level (either by you if your host exposes it, or by your host/admin if they lock it down).
Skin Options (which you found under User Profile) = settings within Evolution itself — things like Layout (Refreshed, etc.), Color Scheme (Light/Dark), Language, table display preferences, etc. These only change how Evolution looks and behaves; they don't switch you to Enhanced.
So the "Skin Options" page you screenshotted isn't where you go back to Enhanced from — that page only customizes Evolution. If you want out of Evolution entirely, you'll need to ask your host to set it for you, since that toggle isn't available in your user-level Skin Options.