I have not actually done this, but it seems like Hydra ought to work acceptably on a Kubernetes cluster. The hydra-server, hydra-evaluator, and hydra-queue-runner daemons can run together as adjacent containers in a pod, probably with a persistent storage volume so build logs stick around. Postgres on kubernetes is doable and thoroughly discussed elsewhere; it gets somewhat complicated if you require high availability, but for a simple setup all you really need is persistent storage. Projects like kubedb can make life easier for HA database setups.
For launching builder instances as pods, hydra-provisioner would be a good starting point. I’m just unsure about the mechanics of connecting them up as trusted remote nix daemons. Perhaps it’s not so different than managing ec2 instances.