Thanks to Ryan in the comments, it appears Amazon has told The Verge that the HBO shows will not be leaving on May 21st, and that the labeling is a mistake that will soon be corrected.
The streaming media landscape has changed quite a bit since Amazon signed a deal nearly 3 years ago with HBO that added a large amount of HBO original shows to Prime Video. That’s probably why the two companies have chosen not to renew the arrangement, so several HBO original shows will be leaving Prime Video on May 21, the 3 year mark of the agreement.
Not all HBO shows will be leaving at once, since not all arrived at the same time. This May 21 seems to be when the first shows to arrive will be leaving. It actually isn’t even entire shows that will leave at once, but rather, individual seasons. Some shows will see their earliest seasons drop off of Prime Video, but seasons that arrived later will remain for another year or two.
Unfortunately, there’s no easy way to see a list of all the HBO shows and seasons that will be leaving Prime Video. There is also no indication on an individual show’s product page either. The simplest way to know if a season of a show will be leaving Prime Video this May 21 is to add the season to your watchlist. Then, visit your Amazon Watchlist page and mouse over the season to see if the “Leaving Prime” orange banner is present within the information that appears.