There are lots of native NixOS tools for managing whole clusters (NixOps, Disnix, Colmena, deploy-rs, Morph, krops, Bento, ...). Lots of people deploy whole fleets of NixOS servers or clusters for specific applications without resorting to Kubernetes. (Kube integrations are also popular, though.) Some of those solutions are very old, too.

Disnix has been around for a long time, probably since before you ever heard of NixOS.

I wouldn't say completely orthogonal. E.g. the points I've cited are overlap between the two, and ultimately both are meant to host some kind of services. But yes NixOS by itself manages a single machine (although combined with terraform it can become very convenient to also manage a fleet of NixOS machines). Kubernetes manages services on a cluster, but given how powerful a single machine can be I do think that many of those clusters could also just be one beefy server (and maybe a second one with some fail over mechanism, if needed).

If the cluster is indeed necessary though, I think NixOS can be a great base to stand up a Kubernetes cluster on top of.