You're not wrong, they depend on an external SQL database, which they access with sqlx.
Briefly, you need to manage metadata for the database. You can write your own raft based solution or leverage existing software like etcd or zookeeper that may not "a relational database". Now you need to deploy them with EBS and reimplement data replication + multi AZ fault tolerance, and it's likely still worse performance than RDS because first-class RDS can typically use internal storage API and advanced hardware. Such a scenario is not software driven.
https://flex-ninja.medium.com/from-shared-nothing-to-shared-...