OK, I kept trying, and below is how I gained access. BTW, I think it’s just a bug in the app. If you have a paid account, and the download link popped up for you, that means you have access.
Anyway, right after you log in, wait until the login window closes and you’re forwarded back to the app. Just before the “coming soon, you do not have access…” popup appears, the window of the application grows a bit, as if it is about to let you in. Right at that moment, just quit the app (cmd+q). Then the next time you open the app, you’ll have access!
If anybody from OpenAI is watching, this is not a “rollout” or access issue. It’s just a bug that needs to be fixed.