I believe I was able to find the issue.
It looks like Azure Storage Explorer isn't copying the SMB permissions when it's doing the copy.
I found THIS blog post that talks about using the --preserve-smb-permissions=true parameter with AzCopy.
When I used Azure Storage Explorer to generate the command for me, added the --preserve-smb-permissions=true to the command and ran the AZCopy command manually, it made the error go away.
Granted, I could have started by writing the AzCopy command from scratch, but where's the fun in that? 🤦♂️