I got this today after contacting support.
Thank you for contacting Pokémon Support.
Unfortunately, the “Processing Registration Data” issue that you’re experiencing is a known issue and has been reported to the Pokémon Global Link development team. They are working hard to resolve the issue as quickly as possible. We have created an FAQ article about this subject, and suggest that you subscribe to the article to receive automatic updates about this issue.
The article can be found here:
Processing Registration Data issue
To subscribe to this topic, please log in to the support portal, and navigate to the article. You'll see a "subscribe" link on the right hand side of the article. Click that and you'll see a confirmation window at the bottom of the page that will confirm the email address that the updates will be sent to.