The HAProxy Data Plane API is an executable (details on GitHub here) that runs alongside HAProxy and provides a REST API that can be used to configure HAProxy whilst it is running, therefore providing a control plane for HAProxy.
If multiple instances of HAProxy are being run, how does one ensure consistency of the configuration across all instances? i.e. if the configuration of one instance is modified via a REST call to the API, how can this change be communicated to all instances?
The Data Plane API is a sidecar process that runs next to HAProxy and manages configuration for a single instance. It does not manage configuration of multiple instances. You would have to make changes to the Data Plane API installed on each cluster member. Thankfully, the Data Plane API supports transactions so you may apply changes in parallel and commit all instances at once should your changes work without exception!