The SDKs -- which do most of the heavy lifting of managing state for you -- are open source. For example the TS SDK (https://github.com/dbos-inc/dbos-transact) runs on node and you can run node anywhere (k8s, VMs, etc.)
With respect to AWS, where we currently host DBOS Cloud, we rent baremetal machines and built the entire hosting layer using Firecracker, Postgres, and other well known frameworks that we can bring to other metal providers (https://www.dbos.dev/blog/anatomy-of-dbos-cloud).