Right at the bottom of the catalogue is a section called “Last chance to play”. Currently there are two games listed: PS4 game Shadow Warrior 3 and PS3 game Syberia. The former is set to leave the Extra catalogue on 5th July 2022 - although it’s been on PS Now since 1st March - while the latter will leave Premium on 19th July 2022. Watch on YouTube Eurogamer Newscast: What can Sony do to improve PlayStation Plus Premium?
Some other games are also showing expiry dates, although they don’t appear in the “Last chance to play” section, only by search - as spotted by Push Square and verified by Eurogamer. They include:

NBA 2K22 - 31st August 2022 WRC 10 - 31st August 2022 Red Dead Redemption 2 - 20th September 2022 Red Dead Redemption - 17th October 2022 Red Dead Redemption: Undead Nightmare - 17th October 2022

Other games not listed in “Last chance to play” may also have an expiration date. PS Plus launched this week in the UK and Europe, exceeding the promised number of catalogued games. We’ve got the full list of games available here.