[TEST] Expose ability to provide http headers when sending requests in our REST tests

ElasticsearchRestTests has now a `restClientSettings` method that can be overriden to provide headers as settings (similarly to what we do with transport client). Those headers will be sent together with every REST requests within the tests.

Closes #7710
Internal: make sure that original headers are used when executing search as part of put warmer

Closes #7711