This issue captures the followup tasks for #142295:

• Merge configurations into a single setting
• Use single logger, look into proper identifying the dataset
• Update docs for the above
• Rename rows to hits for SQL
• Add the shard count on which the query executes - successful, skipped and failed
• Rename include_system_indices to include.system_indices
• Add profiles to ESQL query logging #142618
• Have a boolean indicating whether the query timed out
• Have a boolean that says whether DSL query returned any aggregations