Add integration test to ensure the SavedObjectsRepository handles responses correctly

[TinaHeiligers]

In #107104 we added functionality to determine if 404 responses are a result of saved object documents not being found or some other cause where the response can't be verified to have come from Elasticsearch.

As we implement the differentiation more broadly in all the repository calls to ES, we need to ensure the behavior is consistent.

Adding an integration test would be great but is not simple to do because we'd need to setup a proxy server in front of Elasticsearch that allows us to 'hi-jack' the response to test the condition.

Suggested Implementation

We should experiment with using a custom Hapi server with the h2o2 pluging (the same one we use for the base path proxy).

[elasticmachine]

Pinging @elastic/kibana-core (Team:Core)

[TinaHeiligers]

@elastic/kibana-operations can you give any guidance here?

[tylersmalley]

I have created #107422 to track, but anyone should be able to help out here.