Update 7: I finally managed to speak with Apple Developer Support by phone after waiting on hold for more than 100 minutes. During the call, I was told that my Apple ID will never be able to complete enrollment in the Apple Developer Program. I asked whether there was any specific reason for this decision, but I was told that they were unable to disclose the reason. I also asked whether my case could be escalated to another team or reviewed by someone else. I was told that this was not possible, as I was already speaking with the highest level of support available for this type of issue. Finally, I asked whether creating a new Apple ID would help. The representative said they could not advise me against trying, but they also could not say whether a new Apple ID would be able to complete enrollment. This leaves me in a very difficult situation. My current Apple ID has been in use for many years, is already a member of several Apple Developer Program organizations, and has full access to App Store Connect. However, according to Apple, I will never be able to obtain my own Individual membership. At this point, my only remaining option seems to be creating a new Apple ID and attempting enrollment from scratch. I will post another update with the outcome, whether it succeeds or fails, in the hope that it may help others facing the same situation.

Update 6: I received a response to my Feedback Assistant report (FB23242373). Unfortunately, the response simply instructed me to close the feedback report and refer to my existing Developer Support case (102888399005) and the original email I received from Developer Support. The problem is that the referenced email was only a generic response and did not answer my questions or provide any instructions on how to proceed. I replied to that email the following day with additional details, but I have still not received any further response after several weeks. I understand that Feedback Assistant is probably not the appropriate team to resolve enrollment issues. I submitted the report only because the enrollment state was inconsistent across the website, iOS, and macOS at the time, and I hoped it might help bring attention to my case. This situation has now become quite urgent for me. I have a completed application that is ready for release, and customers are waiting for it. However, I am currently unable to publish it because I cannot complete my Individual Apple Developer Program enrollment. 
If someone from Apple is following this thread, I would be very grateful if my Developer Support case (102888399005) could be reviewed by the appropriate team. As always, if anyone else is experiencing the same issue, I would appreciate hearing about your experience. And if my case is eventually resolved, I will update this thread with the exact resolution so that it may help others in the future.

Update 5: I want to share another update in case it helps someone experiencing the same issue. I contacted Quinn “The Eskimo” from Apple Developer Technical Support directly. He kindly replied and confirmed that my existing Developer Support case is the correct path for resolving this issue. He also mentioned that he was not sure why it was taking so long for the Developer Programs team to respond. Unfortunately, despite that confirmation, there has still been no progress. My enrollment remains blocked. If anyone else has experienced a similar issue, I would really appreciate hearing how it was eventually resolved. Even knowing how long it took or whether your enrollment had to be manually reset would be very helpful. If this thread is being followed by others with the same problem, any interaction or additional reports may help make the issue more visible to the appropriate team. I’ll continue updating this thread, and if my case is eventually resolved, I’ll post exactly what happened and how it was resolved so that it may help others facing the same situation. Thank you

Update 4: The issue remains unresolved. I have now: opened Apple Developer Support request (Case ID 102888399005), submitted Feedback Assistant report FB23242373, and posted here on the Apple Developer Forums. At this point, enrollment remains blocked across all platforms. If anyone from Apple Developer Support is reviewing this thread, could you please confirm whether a failed Individual enrollment can be reset or restarted? I would appreciate any guidance, status update, or confirmation that the case has reached the appropriate team.

Thank you

Update 3: The situation has changed again. Previously, the Apple Developer app on macOS still allowed me to start the enrollment process, although it would either display a completely black image after scanning my ID document or crash immediately. As of today, the behavior has changed. The “Enroll Now” button is now disabled in the macOS Apple Developer app as well, matching the behavior in the iOS app. Current status across all platforms: Apple Developer app on iOS and macOS: “Enroll Now” is disabled and displays the message “Enrollment through the Apple Developer app is not available for this Apple Account.” Apple Developer website: “Your enrollment could not be completed - Your enrollment in the Apple Developer Program could not be completed at this time.” One thing I have noticed is that the behavior of my account has changed several times since I posted this thread. Before posting here, the status remained unchanged for weeks. Since then, different messages and restrictions have appeared across the website and Apple Developer apps. Because of these changes, it appears that someone may be reviewing or processing my enrollment in the background, although I have still not received any response to my support requests or forum post. If someone from Apple who has access to the enrollment system is reading this, I would be very grateful if you could review my case (Case ID: 102888399005) and either: reset or unblock the enrollment process, allow me to restart the identity verification process, or provide any guidance on what is preventing enrollment from being completed. At this point, I am mainly looking for any response, clarification, or next step that would allow me to move forward. Thank you.

Update 2: For additional context, my Apple ID is approximately 14 years old and is already a member of several Apple Developer Program organizations. I have normal access to App Store Connect and existing developer teams. The issue only affects enrollment into my own Individual Apple Developer Program membership.

Update: The behavior has changed now: On iOS, the Apple Developer app now shows a disabled “Enroll Now” button with the message “Enrollment through the Apple Developer app is not available for this Apple Account.” On the web, the enrollment page still displays “Your enrollment could not be completed.” In the macOS Apple Developer app, clicking “Enroll Now” results in an “Action not allowed” error.