While not built in k8s has at least velero and kasten. However they are only possible because of snapshots https://kubernetes.io/docs/concepts/storage/volume-snapshots... and kasten has a plugin like architecture (because of k8s ) that supports application specific backups. However I never found something like that for compose. And that is troublesome in bigger projects like sentry
Docker volumes (and bind mounts) however have the minor problem of being hard to get a consistent copy to without stopping the service. You can work around this by, e. G., having ZFS or btrfs as the underlying FS and making a snapshot there. Otherwise, your software (like PostgreSQL) might also have other online backup tooling.
In my setups it just was easier to use fixed paths (or relative to project dir) from a permissions management perspective. Backup tools did not always have to/should run as root which is helpful on machines providing multiple distinct services.
Putting borg or a similar tool in a container that is part of the compose manifest file can also help. I haven't seen this used in practice though yet.