I created an Issue with Google Cloud support which was recently responded to by suggesting:

To ensure a faster resolution and dedicated support for your issue, I kindly request you to file a support ticket by clicking here. Our support team will prioritize your request and provide you with the assistance you need.

I was logged into my GCloud account as Owner so when I followed the steps in that link to create a new case, it results in “Insufficient Permissions” message and I cannot submit.
So then, inside the GCloud IAM Roles, I added the Tech Support Editor role to my existing Owner account. Now my IAM looks like:

Then I refreshed my GCloud session and tried again to create the new case, again resulting in a permissions error:

Is there something wrong with the Owner or Tech Support Editor when creating a new case with GCloud?