I mostly use postgres so I created myself a small docker image, which has the postgres client, restic and cron. It also gets a small bash script which executes pg_dump and then restic to backup the dump. pg_dump can be used while the database is used so no issues there. Restic stores the backup in a volume which points to an NFS share on my NAS. This script is called periodically by cron.
I use this image to start a backup-service alongside every database. So it's part of the docker-compose.yml