Watched State: Enable Sync Watch State & Ratings
Plex Documentation → Account Information → Sync Watch State & Ratings
It is an account, not server, setting. Have anyone you share with enable it as well. Not supported for Managed Accounts.
Metadata
If you have custom artwork, descriptions, collections, etc., you need to save the Plex Data Folder from the current installation. This also saves watched status and ratings, but it is still a good idea to enable the Sync Watch Status feature mentioned above as a backup.
Use Hyper Backup to make a backup of the current Plex Data Folder. You’ll then restore after re-installing Plex (that’s the high level, there are other steps). Do not just copy the Plex Data Folder to a backup location. Using Hyper Backup preserves file permissions.
See Move an Install to Another System. Be sure to disable Empty Trash Automatically.
The Synology FAQ - Questions, Answers, and How-To’s also has useful information.