How can one understand if a user has used SFMC APIs or SSJS scripts to log in to SFMC?

 Enabling the Audit Trail is essential to find out if SEMC login has happened. 
Email Studio > Admin > Security Settings > Enable Audit Trail Data Collection: Yes.
When the Audit Trail is enabled, it has a REST API endpoint, which looks like this: 
YOURTENANT. Rest. marketingcloudapis.com/data/v1/audit/auditevents.

You can use the REST API endpoint in a script activity and take it to data extension. Some of the properties that are returned are id, employee.id, createdDate, memberId, operation.id, enterpriseId, object.id, transactionId, object.name, employee.userName.