The System.CalloutException with the message "Unauthorized endpoint" typically indicates that the endpoint to which the callout is being made has not been authorized in the Salesforce org's security settings. To resolve this, the developer must navigate to the Remote Site Settings in the Salesforce Setup and add the endpoint URL as a new remote site. This step is necessary to authorize the Salesforce org to send outbound callouts to that specific endpoint. Annotating with @Future(Callout=true) is necessary for making callouts from methods that perform DML operations, but it does not resolve endpoint authorization issues. Similarly, changing the access modifier or using SetHeader() for authentication would not address the unauthorized endpoint error.
References:
Remote Site Settings
Apex Developer Guide: Making Callouts Using Apex