An example unwrapping a (Date, Text.DateStyle) from LocalizedStringKey underlying storage. I'm not sure how to actually format the date with the DateStyle.

DateStyle.swift

@available(macOS 12.0, iOS 15.0, tvOS 15.0, watchOS 8.0, *)
private func stringFromDateStyle(storage: Any) -> String? {
  let dateStyleChildren = Array(Mirror(reflecting: storage).children)
  guard dateStyleChildren.count == 2, let text = dateStyleChildren[0].value as? Text else {
    return nil
  }

  let textStorage = Array(Mirror(reflecting: text).children)[0].value // Text.Storage
  let dateTextStorage = Array(Mirror(reflecting: textStorage).children)[0].value
  guard "\(type(of: dateTextStorage))" == "DateTextStorage" else {
    return nil
  }

  guard let (date, dateStyle) = Array(Mirror(reflecting: Array(Mirror(reflecting: dateTextStorage).children)[0].value).children)[0].value as? (Date, Text.DateStyle) else {
    return nil
  }

  return "???"
}