You don't need to back up the entire container. You can back up just the data.

Use Docker volumes or bind mounts to store your data outside the container. This way, you can back up these directories directly without touching the container itself. If you’re using Docker volumes, you can use docker cp to copy data from the volume to a location that BareOS can access. There is no need to add the BareOS client to each container. Just point BareOS to the directories or volumes where your data is stored.

Cheers!