The database keeps Windows paths in Windows format (including drive letter). Metadata is also different, however finer points (e.g. NTFS ACLs) might not matter. This definitely seems an awkward arrangement.
In terms of requirements, I take it that this is dual-boot, files are changed from both, and backups desired quickly enough that one of the OSs can’t be declared the backup “owner”, and the other will have to wait?
Waiting can be somewhat smoothed over using direct file copying for files newer than Duplicati’s last run, however either a smart copy tool would be needed, or maybe some helper e.g. the Linux find command.
There are also ways to make Linux run more like Windows or vice versa (Windows Subsystem for Linux) however I’m not sure how solid they are. I do see some reports of being able to sort of run mono on WSL.
Just doing redundant backups is not all that bad, in fact some people consider it best practice, although it usually also involves different backup software and destination – where are you if you drop external drive?
Redundant backups even to same destination can help you if Duplicati ever has issues (it can happen…).
The other challenge is that your backups are not the same. The Windows one has a “few others” as well. Even if you somehow manage to share a database (which I doubt is possible), this would confuse things.