I am also waiting for a Genie API.  During one of the product reviews last fall, the presenter said a preview probably in 2025.  Documentation is showing up in the Python SDK (databricks-sdk-py/docs/workspace/dashboards/genie.rst at main · databricks/databricks-sdk-py · GitHu...) for Genie, and there are usable classes in the Java SDK (databricks-sdk-java/databricks-sdk-java/src/main/java/com/databricks/sdk/service/dashboards/GenieAPI...).  However, there is no documentation about a Genie endpoint in the REST API.  It looks like an API preview is on the way but is not yet finalized, best I can say is watch product announcements and maybe try the SDK and see if you can get it to work.