According to this VEEAM article, it's straight forward:
However, it doesn't work because we don't have a full SQL Server license in the VEEAM server.
How can we run a post backup script, from VEEAM, with access to another SQL Server?
The issue for us is sqlcmd
tool is not installed inside the VEEAM service. We would have to install a new version of SQL Server just so we can run T-SQL commands.