Docker: I have configured and authorized rclone. Will the authorization be lost if I rebuild the Docker container?

No. If the backup has already been run with Cloud Backup, BmuS copied rclone.conf automatically from the Docker container to /BmuS-Docker/config, if it was not already there. If the file is already there, BmuS will always use this one, even if the Docker container is rebuilt or updated. The condition is that the path in bmus.conf is correct:

RCLONE_CFG_PATH="/config/rclone.conf"