Hi there, i have been struggling with ITP as well. I did find out that if i set the cookie in first party context first, once storage access is granted i was able to see that cookie and modify it. So probably what would help for you is to first set this cookie in first party context(for example a pop-up, or just the top document), then in third party context (iframe) you will be able to change it.
DavidDamNL
Users receive reputation points by contributing quality content to the forums.
Posts include post and replies published on the forums.
Post authors can mark replies as Accepted to indicate successful solutions.
Apple Developer Forums admins can mark replies as Apple Recommended to indicate an approved solution