If somehow Yandex has a VSS snapshot option, you could try that. If not, some people use Duplicati to backup its own databases as a secondary job after the main backup, using a –snapshot-policy setting such as on. Avoiding the in-use database problem is easy if the backup is just the primary job database (find DB’s path) however backing up the whole folder at one go is trickier (unless you use the snapshot) because some file is typically in use during backup.
Also beware that Duplicati-server.sqlite has passwords and other credentials, so trust where you put it, and consider encrypting it (e.g. Duplicati backup) instead of just making a clear-text copy to the remote location.
[Idea] Backup Duplicati database to avoid recreate
By default everything is there, per --server-datafolder, however if you want you can probably use --dbpath for an individual job database to move it elsewhere, perhaps even to its own folder. I’m not terribly familar with the Database UI buttons, but you could probably also move where the job database is stored like this:
If you want to make changes to the location where the local database is stored, you can use the Reset, Save, Save and repair and Move existing database buttons.
EDIT: Quote was from the manual at the earlier link about DB’s path). Doing the same trick for Duplicati-server.sqlite (the one with the other security cautions) will be harder, however this file doesn’t change as often as the per-job database, is small, and has no Recreate need or ability. Maybe you can just manually copy it somewhere occasionally, e.g. after changing settings. Treat as like a set of job exports plus more.