…trips is true (elastic#117504)

* Fix NPE caused by race condition in async search when minimise round trips is true

Previously, the `notifyListShards()` initialised and updated the
required pre-requisites (`searchResponse` being amongst them) when a
search op began. This function takes in arguments that contain
shard-specific details amongst others. Because this information is not
immediately available when the search begins, it is not immediately
called. In some specific cases, there can be a race condition that can
cause the pre-requisities (such as `searchResponse`) to be accessed
before they're initialised, causing an NPE.

This fix addresses the race condition by splitting the initialisation
and subsequent updation amongst 2 different methods. This way, the
pre-requisities are always initialised and do not lead to an NPE.

* Try: call `notifyListShards()` after `notifySearchStart()` when minimize round trips is true

* Add removed code comment

* Pass `Clusters` to `SearchTask` rather than using progress listener to
signify search start.

To prevent polluting the progress listener with unnecessary search
specific details, we now pass the `Clusters` object to `SearchTask` when
a search op begins. This lets `AsyncSearchTask` access it and use it to
initialise `MutableSearchResponse` appropriately.

* Use appropriate `clusters` object rather than re-building it

* Do not double set `mutableSearchResponse`

* Move mutable entities such as shard counts out of `MutableSearchResponse`

* Address PR review: revert moving out mutable entities from
`MutableSearchResponse`

* Update docs/changelog/117504.yaml

* Get rid of `SetOnce` for `searchResponse`

* Drop redundant check around shards count

* Add a test that calls `onListShards()` at last and clarify `updateShardsAndClusters()`'s comment

* Fix test: ref count

* Address review comment: rewrite comment and test