Query rewrite refactoring

[salvatore-campagna]

Description

This refactoring is a prerequisite for #96161. The idea is to cleanup the code in order to make sure we have a better structure around the way we use QueryRewriteContext and SearchExecutionContext. Both of them are used by the rewrite logic to simplify queries and improve query execution latency and resource usage.

We would like to enable the following three scenarios:

1. Rewrite happening on the coordinator which requires the QueryRewriteContext and a few more information but not requiring a SearchExecutionContext. This is the case for rewrite operations which happen entirely on the coordinator node and spare us from executing the query on the data node.
2. Rewrite happening on the data node which requires the QueryRewriteContext and some information available in the SearchExecutionContext. In some scenarios an IndexSearcher is not required. Not using it saves us a few unnecessary IO operations and allows us to complete query execution before we even need to read the index.
3. Rewrite happening on the data node which requires the QueryRewriteContext and the full SearchExecutionContext. In this scenario an IndexSearcher is required for the rewrite logic to be fully exploited.

For this reason we will refactor the SearchExecutionContext pulling up into the QueryRewriteContext a few fields/methods (like getFieldType and getIndexSettings). Moreover, we will need to revisit the implementation of doRewrite for subclasses of AbstractQueryBuilder in such a way to enable the three rewrite logic branches described above.

[elasticsearchmachine]

Pinging @elastic/es-search (Team:Search)

[martijnvg]

Not using it saves us a few unnecessary IO operations

Maybe also mentioning avoiding do refresh in case shard is search-idle?