How to connect to github repository for organization (enterprise standard github license)

From your description, I guess you are following this approach and created a sort of custom M extension to connect to github 

https://learn.microsoft.com/en-us/power-query/samples/github/readme

Have you tried using the Web connector and with the authentication mode as Personal access token, if not then please go through this 

https://smootherconsulting.com/learn/connect-power-bi-to-private-github-repo

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