dblink_error_message fetches the most recent remote error message for a given connection.
When asynchronous queries are initiated by dblink_send_query, the error message associated with the connection might not get updated until the server's response message is consumed. This typically means that dblink_is_busy or dblink_get_result should be called prior to dblink_error_message, so that any error generated by the asynchronous query will be visible.
Read the upstream documentation. For corrections, first check the current version.