I am not aware of a end of life for IMAP or POP currently being planned by anyone anywhere in the known space time continuum.
There are planned retirements for Basic Authentication (by Google and Microsoft). Which has nothing to do with POP or IMAP (protocols) and does have to do with the Basic Authentication protocols. Both of these retirements were both postponed due to Covid. The devs have also stated here on the forums and github that they will have a solution in place in osTicket prior to the new cut off dates. So all you will have to do is upgrade osTicket to the new version when it comes out (or possibly install a new authentication plugin).