refactor: extract ES-compat handler logic into reusable pub(crate) functions (#6271)

Extract JSON construction from warp handlers into standalone functions
that can be called directly without HTTP, enabling non-HTTP consumers
(e.g., gRPC passthrough) to reuse the ES-compatible logic.

Extracted functions:
- es_compat_cluster_info, es_compat_nodes_info, es_compat_search_shards,
  es_compat_aliases, es_compat_cluster_health_check, es_compat_delete_scroll

Made pub(crate): es_compat_index_mapping, es_compat_index_search,
es_compat_index_count, es_compat_index_stats, es_compat_cat_indices,
es_compat_index_cat_indices, es_compat_resolve_index,
es_compat_index_field_capabilities, es_compat_index_multi_search, es_scroll

Also made model and rest_handler modules pub(crate) in mod.rs.

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>