Function run_router_search 

pub async fn run_router_search(
    registry: Arc<ProviderRegistry>,
    router_model: &str,
    query: &str,
    top_n: usize,
) -> Result<RouterResult>

Execute the full search pipeline.

Picks up to top_n backends from the router’s plan (1 when the caller wants a single best hit; >1 for fan-out).