Regarding your first issue with changing the region of a resource group, it's important to note that the region of a resource group is determined by the region of its contained resources. If you're unable to change the region of the resource group even though all the resources within it are in the desired region, it could be due to dependencies or limitations within Azure. I recommend verifying that all resources within the resource group support being moved to the desired region and that there are no dependencies preventing the change.
For your second issue concerning the movement of function apps from one resource group to another within the same region, it's unusual that Azure indicates the resources have been moved but they do not appear in the target resource group. This could be a temporary issue or a result of a misconfiguration. I suggest checking the Azure Activity Log for any error messages or failure notifications related to the resource movement. Additionally, ensure that the destination resource group exists and that the appropriate permissions are set to allow the movement of resources.
If these steps do not resolve your issues, please provide more details, and we'll be happy to assist you further.