I’m currently on v1.20.3.3483 and there’s a new version v1.20.5.3600 but every time I downloaded the new version and try to install it, nothing happens. I re-open Plex and the same messages with the same version to upgrade is there.
It sounds like there may be an issue shutting down PMS for the update to work. Try shutting down PMS manually and making sure in the task manager that all Plex related programs have stopped. Then run the installer.