Currently the Connector Details API returns warnings in the following format.

"warnings":[
            {
               "code":"duplicate_custom_field_names",
               "message":"Duplicate custom field names"
            },
            {
               "code":"jira_project_issues_error",
               "message":"An error occurred for some projects"
            }
          ]

Here, the warnings contain very little information about the details of the errors as compared to the information present on the Connector Warnings page. 

Currently one will have to necessarily visit this page to get these details. A user may want to get these details via the Connector Details API and add them to an automated alerting system. This is just one of many use cases. Getting detailed error messages in the API response would be helpful.