For a government agency implementing an eSignature solution with DocuSign, the optimal approach to polling the status of signed envelopes involves using DocuSign's REST API. This API provides endpoints for querying the status of envelope transactions, enabling real-time updates on the eSignature process. This method allows for the integration of Salesforce with DocuSign's services, ensuring that the status of each envelope is accurately reflected within the Salesforce system. Utilizing the REST API for this purpose leverages the direct communication between Salesforce and DocuSign, providing a robust and efficient solution for tracking eSignature statuses in compliance with the agency's nonfunctional requirements.