I paid for a membership today through the Developer app and used my passport as my identifier. As of this writing, no approval. In the app. the Enroll Now button is disabled, and right under it I have a hint saying: "You'll receive an email soon.".
I'm a little less worried seeing that other folk are also having trouble getting signed up, but this is still concerning.
Topic:
Developer Tools & Services
SubTopic:
Apple Developer Program