The issue not how to access private posts. The issue is that the empty group_* result I posted initially only occurs if I set the page to private and access it as described in that stackoverflow answer.
This an example command I use for testing where it fails as described above.
curl -k --user user:passwd "https://myapp.local/wp-json/wp/v2/pages?_embed"
As already mentioned if the page is set to public then it works as expected.
