What do you mean by and then in Docker Exec with container running ... ?
What output is reported when running the virtuoso-t +foreground +restore-backup backup or virtuoso-t +restore-backup backup commands ?
How have you created this custom Docker virtuoso image/container ?
Please provide the actual text output of the commands being so we can see what you are doing.
A default Virtuoso docker container will automatically shutdown when the Virtuoso server is gracefully shutdown or automatically restart if the database shuts down and so cannot be restored from a backup, which requires the database be shutdown and the a terminal session to the container to run the restore backup command.
What you can do is to start Virtuoso Docker image in bash shell with existing database volume mounted as detailed in the post such that the Virtuoso container can be accessed as a standalone installation and started & stopped manually. Which will enable the normal Virtuoso backup and restore commands to be run.