Quick follow up tasks mostly around tests for after #121885 lands, covering what isn't tracked in the rollout doc:

• Fix tests running rest-api-spec/src/yamlRestTest/resources/rest-api-spec/test/search/120_batch_reduce_size.yml (Add IT for num_reduced_phases with batched query execution #134312)
• Adjust SearchErrorTraceIT/AsyncSearchErrorTraceIT and remove batched execution override (Fix SearchErrorTraceIT and friends to work with batched query execution #132227)
• Adjust TransportSearchIT and remove batched execution override. Edit: must fix underlying bug in how batched queries raise phase failures.
• Adjust TasksIT and remove batched execution override (Update TasksIT for batched execution #132762)
• Adjust SearchCancellationIT and remove batched execution override (Rework cancellation test for batched query execution #133579)
  • [ ] Optimise failure path if no partial results are requested in org.elasticsearch.action.search.SearchQueryThenFetchAsyncAction#executeShardTasks (edit: doing this may fix SearchCancellationIT)
• Adjust TermsDocCountErrorIT and remove batched execution override. Edit: must fix underlying bug in the calculation of doc count error on batch-reduced aggregations. (Fix terms aggregation doc_count_error_upper_bound for already reduced results (batched query phase) #134645)