To identify the misconfiguration with the least operational overhead, the network engineer should use the Route Analyzer feature for AWS Transit Gateway Network Manager. This feature allows for the analysis of routes within the transit gateway, making it straightforward to identify missing or incorrect routes without the need for additional logging or packet capturing. Options B, C, and D involve more complex setups and additional operational overhead, such as setting up IP monitoring, analyzing VPC flow logs, or using traffic mirroring for packet captures, which are not necessary when the Route Analyzer can directly provide the needed insights.