If it's any consolation, I have exactly the same issue. I took delivery of my ID.3 on Friday and have not been able to get the We Connect ID working. The enrolment all went through, but I receive no data in the app and all the Mobile Online Services have the red exclamation mark like yours, stating "You have no contract for mobile online services".
I've been in contact with support by email and have followed all their instructions (most of which I had already tried) including essentially resetting everything to defaults and re-pairing it in an area of good cellular coverage but to no avail.
They have apparently escalated to their engineers in Germany and I've heard no more yet.
I have the same issue as well picked up last week and not been able to get the app working got the same issue with the no active contract, the support told me they are aware of the issue and the engineers are looking to push a fix for it but they did not say how long this would take to sort.
As you say, it's interesting that putting the car in and out of "Offline Mode" immediately shows up in the app, so the enrolment is clearly successful because there is end-to-end communication. Hopefully it's something simple such as a bunch of VIN numbers escaped being automatically assigned with a 3 year subscription, which would hopefully be quite easy for them to resolve.
I have exactly the same problem. I took delivery last Thursday and have tried uninstalling and reinstalling the app. I have the same red exclamation marks against everything.
I just had a reply to my case with VW where they confirmed that they should have fixed the issue. Nothing was immediately apparent in the app, so I removed the car and re-enrolled it using the QR codes and after a minute or so it all sprang to life as it should!
Whether this is specific to my case (and VIN) or whether it's fixed as a whole remains to be seen. Might be worth giving it another go and see if it's fixed for anybody else!