There are a couple of independent drivers such as Reactiverse's reactive-pg-client. These drivers come with a vendor-specific API and aren't really suited for broader adoption. Client integrators would need to provide additional layers to expose a common API. New drivers cannot easily be plugged into the client library. In contrast, having a standard API would allow pluggability while decoupling clients from database specific solutions – a huge value for all.
Oracle announced ADBA, which is an initiative to provide a standardized API for asynchronous database access in Java by using futures. Everything in ADBA is a work in progress, and the team behind ADBA is happy to get feedback. A bunch of Postgres folks is working on a Postgres ADBA driver that can be used for first experiments. PgNio is another asynchronous driver for Postgres that started experimenting with ADBA.
https://spring.io/blog/2018/12/07/reactive-programming-and-relational-databases