Reading Parental Control settings in iOS

Nope, unfortunately there's no API access to restrictions and parental controls.

Parental control settings can be read with UserDefaults

UserDefaults.standard.object(forKey: "com.apple.content-rating.TVShowRating")

The value of this object ranges from 0 to 1000.

Content rating keys that can be read:

com.apple.content-rating.ExplicitBooksAllowed
com.apple.content-rating.ExplicitMusicPodcastsAllowed
com.apple.content-rating.AppRating
com.apple.content-rating.MovieRating
com.apple.content-rating.TVShowRating

More about what the values mean can be seen in the
Apple developer documentation: Respecting Restrictions