If, however, you had other database-related needs you didn't mention — e.g. being able to arbitrarily join the state data of this system as dimension data in OLAP queries on other, non-scheduler-y tables in that DB — then your constraints probably did indeed make using a DBMS the best choice here, despite the scaling challenges.
(Also, funny enough, I am myself in the middle of writing a cluster-workload-manager as a custom in-memory Elixir daemon! But that's with the unique constraint of needing lightweight, realtime prioritization of workloads, each backing synchronous HTTP RPC requests. Having millions of teeny-tiny jobs that are usually over in milliseconds [but which can sometimes run for multiple minutes], isn't something any HPC-targeting workload manager is really architected for.)