AzCopy is preinstalled and built into Azure Cloud Shell. Azure Cloud Shell team will periodically perform updates of these applications and they will automatically be updated for you.
If you absolutely need to run the latest version you can download the Linux version and run it from your home directory.
wget -O azcopy_v10.tar.gz https://aka.ms/downloadazcopy-v10-linux && tar -xf azcopy_v10.tar.gz --strip-components=1
./azcopy --version
I confirmed this version will work in either PowerShell or bash for Azure Cloud Shell.
Hope this helps! Let me know if you still have questions or need further assistance.
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