I suggest you connect Mendix to Amazon S3. They have a good pricing / GB and seamless integrate with Mendix:
Yes Azure can be used too,
I don't have any personal experience with the Mendix hosted services in Azure cloud.
With one my clients us using a Mendix hosted environment with both Azure as AWS for file storage (>10TB), wich can be accessed through connectors. like https://appstore.home.mendix.com/link/app/2074/Mendix/Amazon-S3-Connector with the connectors you need to write your own logic.
Something to take in account with the use of the connectors, is the upload and download of the files should not go trough the Mendix server.