In the AWS Elasticsearch documentation they recommend submitting Elasticsearch requests using the AWS SDK. However, I don't find any APIs related to indexing and searching in the SDK. Should indexing and searching instead be done through one of the Elasticsearch client libraries?
The AWS SDK will provide methods to manage the Elasticsearch service (create new domain, list domains, add tags, etc). You will need to interface with Elasticsearch either through a client library or simple HTTPS requests (POST, PUT, GET).