I think there are some challenges here.
docker executable and related commands are not present within the standard Duplicati container. If they were (if you put them there), then you’d have to map the docker engine socket from the host to the Duplicati container so that the Duplicati docker container
docker command would work as if it was being run on the host.
This seems a bit messy. I wouldn’t advise modifying a docker container because every time you update to a new version you’d have to repeat your customizations.
Maybe a simpler solution is to just schedule the host to run the commands on a schedule similar to your Duplicati backup schedule?