Hi @chaserb
You are using the wrong type of API key.
The docs you referenced are to create an Elasticsearch "Service" API key to operate on elasticsearch deployments in other words, API key to allow you to create, update, delete deployments not an API key to work on the data within a deployment.
For the operation you are trying...the elasticsearch normal REST APIs you need to create a "normal" API KEY from within Kibana
Or directly from the Security REST API
Two entirely separate APIs
One to work CRUD entire elasticsearch deployments
And the normal elasticsearch APIs that work within an elasticsearch cluster