@Bradley Soverns Are you talking about logical backups that you take on flex or managed service backups? You cannot move managed service backups as no one has access to them except Microsoft, If it is a logical backup then all best practices that are applicable for moving files to blob will apply here
https://learn.microsoft.com/en-us/azure/dms/tutorial-postgresql-azure-postgresql-online-portal
Please let me know if you have any other questions.
Regards
Geetha