The menu also has options to share subscriptions with the family and enable renewal receipts.
However, as noted by MacRumors, it seems that the refreshed interface of the Subscriptions menu is only available for devices running iOS 15.5 or later (which also includes iOS 16 beta).iOS 15.4 remains with the old interface even though Apple has updated the Subscriptions menu remotely for iOS 15.5 users.
The Mac also has a Subscriptions menu that is available within the App Store, but this one hasn’t been updated yet.