Function write_distributed_read_routing_report 

pub fn write_distributed_read_routing_report<W: Write>(
    writer: &mut W,
    format: RoutingReportFormat,
    report: &DistributedReadRoutingReport,
) -> Result<()>

Write the report to a caller-provided stderr writer. No StreamingWriter or SQL row formatter is involved, so table/JSON/CSV/TSV/JSONL stdout stays byte-for-byte independent from routing diagnostics.