Can I restore a SQLServer db from URL but not from azure? I have backups in S3.  If I create presigned URLs, can I restore directly from the URL to my on premise SQL Server instance?
No, the FROM URL syntax of the restore command is meant only to work with Azure.  You must find another way of restoring the backups from Amazon storage.

Unfortunately, I don't know much about Amazon's offerings, but did find.


You can mount the storage as a drive in windows.  Then restore from
that. 
Does Amazon offer an SMB accessible storage solution much like
Azure Files?


But failing those, you will just need to copy locally and then restore.  But this is probably your best bet anyways, as you want to avoid involving delicate restore operations with pulling (supposedly large) files across the internet.  By doing this in two distinct steps, you can more easily identify where it failed.