[8.16] Updates ELSER documentation to use 'elasticsearch' service (backport #2866)

[mergify]

Overview

This PR updates the ELSER conceptual documentation to replace the deprecated elser service with the elasticsearch service in the deployment example. The PUT inference API call now specifies the elasticsearch service along with the model_id required for deployment.

Related issue

https://github.com/elastic/search-docs-team/issues/216

Preview

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This is an automatic backport of pull request #2866 done by [Mergify](https://mergify.com).

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