[Search Pipeline] Expose Search Pipeline Stats in Search Response

[mingshl]

Is your feature request related to a problem? Please describe.

Extending from the discussion from adding ignoreFailure to Search Pipeline 8373 ,

In the GA of Search Pipeline, the response from any pipelines(search pipeline/ingest pipeline) will look like the same response as other search response.

So we can NOT tell if a response has gone through the ignoreFailure is True and catching Exceptions, and that is also similar to the existing design of ignore Failure in the ingest pipeline here

The search pipelines stats does gather stats for all requests using pipeline API. And the response from the stats look like this .

Open up this issue to discuss a good way to inform users/consumer about the information from the search pipeline in the search response, for example, the pipeline name, the number of processor within the pipeline, the processor's name, is it ignoreFailure, the failure processor count.

Describe the solution you'd like
Add the stats per request to the search response

Describe alternatives you've considered
or better way to expose the search pipeline metrics

[msfroh]

See also #6794