Function render_a2ui_tool 

pub fn render_a2ui_tool(catalog: Option<&Catalog>) -> ToolDefinition

The inner structured-output tool: emit the surface.

The schema restates the adjacency-list rules, because the model filling it in is the one that has to get them right: a flat list, ids not nesting, exactly one root.

Pass a catalog to name the permitted component types in the schema, which keeps the model inside them without relying on the prompt alone.