The Play button here works as expected - playing through the Recently Added content as listed below it. The Shuffle button, on the other hand, shuffles the entire Library (and shows as “Library” if you go back to Recent Plays.)
Oof… Yes, I have my own Recently Added Smart Playlist with a limit on the age but I still feel this design choice is very counter-intuitive. While I accept your rationalisation, it’s unexpected behaviour (unless “you think about it”) which isn’t great UX. The word “Recently” has implications above and beyond “Ordered by Date Added” which this behaviour doesn’t support.
In the Plex Web App you have the option to choose the number of “Weeks to consider for Continue Watching” and I (as a generic user) would expect implicitly, or ideally explicitly, a similar limit to be put on something entitled “Recently”.