Perhaps the path mapping is just not correct?
I found the Problem. It seems like the Azure Linux Hosts for WebApps does not fully support SMB 3.0, which is needed by Azure File Share mounts. So if you have a correct path mapping there will be error messages on Mongo DB startup and if you screw up the path mappings, all files are stored in the container.
I fixed the Issue by setting up the MongoDB in an azure container instance (ACI), which supports SMB 3.0.
@Sebastian I will update the Azure Documentation again with this new insight and send you a Pull Request
Assets and Mongo db files are not being stored on Azure file storage
Awesome, thanks for your contributions