Sorry, it seems I was sending you down the wrong path.
The 2 authorization mechanisms you are trying will not work for JSM customers, only for JSM agents. Basic authorization only works with API tokens but customers often do not have full Atlassian accounts where they can manage API tokens. And, support for enabling customers with OAuth 2 (3LO) access to APIs is an open feature request:
https://jira.atlassian.com/browse/JSDCLOUD-4065
To my knowledge, a client can only “act as customer” with user impersonation for Connect Apps.