See Migration to new PC - faq wanted and Restoring Duplicati after a Windows system reinstallation
Moving Duplicati databases is the key to avoiding database Recreate time (and maybe other issues).
After migration, the new server can continue backup and keep all history, but don’t let old one backup.
300 GB is not too huge. Do you have any time window for migration with original server unchanged?
You’ll either need to do it in one shot, or find and move later changes with rclone or maybe robocopy.
EDIT: Depending on your files, finer points like permissions might matter, which complicates copying.