I added my files and commited with no problem.
The problem is that when I press "Publish to Github" the only options there appear are private and public repositories as individual.
But I would like to publish as an organization.

I added my files and commited with no problem.
The problem is that when I press "Publish to Github" the only options there appear are private and public repositories as individual.
But I would like to publish as an organization.

Workaround for the lack of functionality:
You can add your project to a local repository by pressing "Initialize Repository" in your "Source Control" tab.
After that, go to Github and make a new empty organisation repository.
Now you can hit F1 and type "Add Remote". You can now choose "Git: Add remote..." and then paste the repository's URL, instead of adding from Github.
Now committing and pushing should work as expected.