Below is a ready-to-use script. Review and adapt variables to your environment.
#!/usr/bin/env bash set -e STACK="mystack" BACKUP_DIR="./compose-backups/$(date +%F)" mkdir -p "$BACKUP_DIR" docker compose -p "$STACK" down tar czf "$BACKUP_DIR/$STACK-volumes.tgz" /var/lib/docker/volumes docker compose -p "$STACK" up -d