I posted this after spending a few hours trying to solve it, and of course 20 minutes after submitting the post I figured it out. I will share why this happened, and how I solved it.
When I tried to publish my GPT as public, the full error that is displayed is as follows:
-‘Public actions require valid privacy policy URLs. Click here to update.’
When you click the ‘Click here’ link, it creates a new Action, whish is where I thought you had to create the Privacy Policy definition. THAT IS NOT CORRECT. You just have to go to your existing defined Action, and add the privacy policy URL at the ‘Privacy policy’ section at the end of the Action definition.
I hope this helps others!