Check the version available via plex.tv and manually download if necessary.
https://www.plex.tv/media-server-downloads/#plex-media-server
PMS 1.16.1.1246 is the first 1.16.1 release. It was released on 19 June and is still considered beta.
Check Server Update Channel
in Status -> General. If set to Public, PMS would still show up to date. If set to Beta, the availability of the update may not have filtered down to your system yet.
You can subscribe to the Plex Media Server announcement to be notified when a new release is available. Scroll to the bottom of the thread and change “Normal” to “Watching.”