Hi Mike Henson,
I don't think the issue is related to the "Publisher" extension in your PRO but likely to your ArcGIS account type.
There are 2 type of AGOL Account:
1. Public Account: You can't publish from PRO
2. Organizational account:
you must be Level 2 - Creator.
If you are creator but still you can't publish it probably means that your administrator revoked this functionality, you can ask to grant it for you by modifying your role.
If I login with the account I am writing right now, I get the same Warning as yours because is a Public account.
With my Organizational account, I publish content without any problem.
Hope it helps.
Pan