You can copy the primary database file over to the new server, to achieve that.
BUT, here’s the rub:
If, on the old server, not all your movies were matched with the same metadata agent, at least some of them will change their “identity” on the new server. Which makes the “watched” status that is still stored in the database obsolete.
If you know your way around a SQL database, you could go and edit the database, to change the old Windows-style file paths (D:\Movies.…) to their proper Linux-style counterparts which are valid on the new server. This makes it more likely for the items to retain their “match”.
See [HowTo] Plex database modification - Moving media the right/wrong way - #10 by jelwell
