gsutil supports copying files from S3 to GCS like mentioned in this blog. Does gsutil tool also supports copying files from Azure?
Gsutil supports transfers from Amazon only, for the time being.
However, it is possible to use third party software like Rclone that is available for many platforms. You can use it to synchronize files and directories.
Also to transfer files from Azure, you can use Azure Data Factory custom activity like explained in this thread and Azure documentation.