Yes, there is definitely some overlap. Kubernetes will help you with the restart and to deliver network packets to the right process. It's also programmable. On the other hand, you have to manually craft the process APIs to communicate and they look very different from the in-process APIs for most languages. You have to think about exposing metrics to some external system that collects them. That and logs are about it for introspection. The rest you have to build yourself.

On the plus side, out of the box it can do things like "run this process N times", "don't run these on the same node", "run this on every node exactly once".

I'd like to get some experience on a real distributed project in Erlang. Mostly in order to be able to assess how big a productivity booster it really is. :-) But it's a chicken and egg problem. Not a hugely popular language <-> fewer developers <-> higher risk for the company.