Look up persistent volume claims and dynamic provisioning. If you cluster is properly configured, then you are one yaml file away from having that. By "configured properly" this means having the correct cloud provider set, otherwise it cannot talk to the APIs.

To be fair, this stateful containers in general are a relatively new thing in K8s and support has been improving.

Also, K8s is trying to do and abstract away a lot, it is more like a distributed operating system by itself. So it is more complicated than swarm.