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Options in backing up persistent docker volumes?
Use bind mounts instead of docker volumes. Then you just have normal directories to back up, the same as you would anything else.
In general, it's not a problem to back up files while the container is running. The exception to this is databases. To have reliable database backups, you need to stop the container (or quiesce/pause the database if it supports it) before backing up the raw database files (including SQLite).