Parent: #3401

Summary

Remote table APIs need the same nested field-path behavior as local tables for create index, search, list, and stats.

Scope

• Define remote request/response semantics for nested field paths and escaped paths.
• Fix Index::Auto or make its nested-field limitations explicit.
• Ensure explicit remote create-index requests preserve canonical field paths.
• Align remote list_indices(), index_stats(), vector search, and FTS query behavior with local tables.

Acceptance criteria

• Remote scalar/vector/FTS index creation accepts nested field paths where local does.
• Remote list/stats responses return canonical full paths.
• Remote explicit vector and FTS search can target nested fields.
• Local and remote tests share the same field-name matrix where practical.