I had exactly the same issue.
Finally I got it working:
- Delete the current ResourceGroup, Resource and the Abonnement
- Create a new Abonnement
- Create a new Bing Search v7 resource with a new resource group
- Use this new Bing Search v7 resource
Somehow, the Azure portal still shows me my old Abonnement, seems to be updated really slow.
Also, the new key of the instance was not working right away, I needed to wait ~5min. after the creation to have a successful API call.