Surface detailed/internal timings from Elasticsearch

It would be valuable to have more detailed and/or internal timings about Elasticsearch search requests, rather than just timings from the perspective of the client.

The profile API returns how much time is spent doing what on each shard, but it has a lot of overhead and doesn't give a great timeline of a search.

We can collect use cases and list them here and see what is feasible and what is needed from other teams to make it happen.

Examples:
- Show how much time is spent networking between nodes
- Show different phases/timings of a search request, e.g. `canMatch`
- Show how long a search task was stuck in a queue