[Search service] Integrate with aborted$ event to cancel discarded requests

[lukasolson]

Waiting on #44302 (PR: #55061), #48811 (PR: #53057).

In the legacy platform, the endpoints that the search APIs hit would listen to HapiJS's disconnect event. However, it was not exposed in the new platform (thus the issue raised above).

When #55061 is merged, we will need to update the search service to take advantage of these events and properly abort the requests to Elasticsearch (in both the sync and async strategies).

Note: We should also add integration in other places we are cancelling requests that are in the new platform, like KQL value suggestions (see #51411, #54451).

[elasticmachine]

Pinging @elastic/kibana-app-arch (Team:AppArch)