> Is LXD's purpose the same as Docker/Kubernetes?

It did occupy the same space including Proxmox.

Back then KVM, Proxmox, VMWare, OpenVZ, LXD, etc were all ways of virtualization.

Whilst it's not exactly the same purpose most companies have or have been shifting to docker and kubernetes and in the cloud vs running their own VM infrastructure.

> Docker is for stateless containers

Tell that to people that run databases with docker and kubernetes. It is a thing and even commercial products are built that way.