Let Settings API be used also for non admins

[maorb]

Hi,

There's the great  Settings API that really helps creating some option pages in site. Anyway, the API must use the options.php on the form's action on order to work. That means that only admins (or users with manage_option capability) can save options to these pages. It would be great letting users with other capabilities to save such option pages, but without them having full access to whole options of the site. It would be great enhancement to the Settings API if could assign who can save custom option page without need to have full manage_options capability.

See #14365