As the old In-App Purchase is stuck in "Developer Action Needed" and no change to any of the metadata resolves that status, I have now created a completely new In-App Purchase in AppStore Connect and verified that it synced to Xcode and showed up correctly in my app.
I then created an archive of the app, selected that archive with the new (working) In-App Purchase and submitted both for review.
After confirming the submission, the In-App Purchase is gone from Xcode again and therefore not visible in my app anymore (which likely will result in a rejection again). In AppStore Connect, the IAP is now "Waiting for Review".
I have just submitted a request to the contact form, including a screen recording I took.