Technically the remote side already does have everything needed to do a restore. The local database can be rebuilt - if needed - by reading existing backup data on the remote side.
That being said, I do something similar to what you are suggesting. I have a second backup job set up in Duplicati whose sole job is to back up the database from the first job. Even though this isn’t technically necessary, I think it can possibly be faster than doing a database rebuild the “normal” way.
I don’t see how you can do this type of backup without setting up a second job though. With only one backup job the database itself is being modified/updated while that job is running. How can it back up the database while at the same time updating it? Even if it did, you wouldn’t be able to restore the database without first having a local database to begin with.
That’s why you either need to back it up using a second backup job, or use a method other than Duplicati to protect the database (which could be triggered automatically at the end of the backup job).